Seventh Viennese Workshop on - SWEETsweet.ua.pt/delfim/delfim/Transparencies/Abstractband.pdf · Eighth Viennese Workshop on Optimal Control, Dynamic Games and Nonlinear Dy-namics:

Eighth Viennese Workshop on Optimal Control, Dynamic Games and

Nonlinear Dynamics: Theory and Applications in Economics

and OR/MS

Vienna, May 14-16, 2003

P R O G R A M A N D

A B S T R A C T S

Responsible for the content: Organizing committee of the 8th Viennese Workshop Design and Layout: Christian Almeder Reproduktion: Digitales Druckcenter WLK Background image, showing the first simultaneous occurrence of limit cycles and DNS-curves, taken from: Josef Haunschmied, Gustav Feichtinger, Richard F. Hartl, and Peter M. Kort: Keeping up with the technology pace: a DNS-curve and a limit cycle in a technology investment decision problem, working paper.

Eighth Viennese Workshop on Optimal Control, Dynamic Games and Nonlinear Dy-

namics: Theory and Applications in Economics and OR/MS

Vienna, May 14-16, 2000

Conference Location:

Industriellenvereinigung Haus der Industrie (Federation of Austrian Industry) Schwarzenbergplatz 4 1030 Wien

Lecture Rooms:Kleiner Festsaal

Arthur-Krupp-SaalLudwig-Urban-Saal

Neuer Saal

Conference Secretary:

Wednesday – Friday 8:30 – 16:30 +43-(0)1-71135/25432 computers with internet access are available.

International Program Committee: • Jess Benhabib, New York University • Carl Chiarella, University of Technology, Sydney • Herbert Dawid, University of Vienna • Engelbert J. Dockner, University of Vienna • Gustav Feichtinger, Vienna University of Technology • Richard F. Hartl, University of Vienna • Cars Hommes, University of Amsterdam • Peter M. Kort, Tilburg University • Kazuo Nishimura, Kyoto University • Suresh P. Sethi, University of Texas at Dallas • Gerhard Sorger, Queen Mary College, University of London • Franz Wirl, University of Vienna

Organizing Committee: • Gustav Feichtinger, Vienna University of Technology • Richard F. Hartl, University of Vienna

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SOCIAL PROGRAM

Tuesday, May 13, 6 - 9 p.m.: Registration and informal get-together at the

Vienna University of Technology, main building, A - 1040 Vienna, Karlsplatz 13

(sponsored by the Vienna University of Technology)

Wednesday, May 14, 8 p.m.: Reception at the Vienna City Hall (Stadtsenatssitzungssaal

A-1010 Vienna, Rathaus (by invitation of the Mayor of Vienna)

Friday, May 16, 7 p.m.:

Reception at the University of Vienna, main building A-1010 Vienna, Dr. Karl Lueger-Ring 1 (sponsored by the University of Vienna)

The workshop is supported by our sponsors:

Austrian Computer Society

Austrian Science Fund

Austrian Society for Operations Research

City of Vienna (Mayor of Vienna)

Federation of Austrian Industry

Imperial Tours

Raiffeisen Capital Management

Vienna University

Vienna University of Technology

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Wednesday, May 14, 2003

09:00 - 09:30 OPENING ADDRESS - KLEINER FESTSAAL 09:30 - 10:30 PLENARY TALK (Chair: Dawid) - Kleiner Festsaal 09:30 - 10:30 Day: Coordination in An Abstract Adaptive Economy 10:30 - 11:00 COFFEE BREAK 11:00 - 12:30 SKIBA 1 (Chair: Hartl) - Kleiner Festsaal 11:00 - 11:30 Semmler, Grüne: Using Dynamic Programming with Adaptive Grid Scheme for

Optimal Control Problems in Economics 11:30 - 12:00 Dawid, Deissenberg: On the Efficiency-Effects of Private (Dis-)Trust in the

Government 12:00 - 12:30 Wagener: Skiba regions and heteroclinic bifurcations 11:00 - 12:30 OPTIMAL CONTROL THEORY (Chair: Maurer) - Ludwig-Urban-Saal 11:00 - 11:30 Leitmann: A Direct Method of Optimization and Its Application to a Class of

Differential Games 11:30 - 12:00 Torres: The Noether Principle of Optimal Control 11:00 - 12:30 MACROECONOMICS (Chair: Kaas) - Arthur-Krupp-Saal 11:00 - 11:30 Neck, Stieber: Tradeoffs of Austrian Budgetary Policies: An Optimum Control

Analysis 11:30 - 12:00 Neck, Behrens: A Macroeconomic Policy Game in a Monetary Union 12:00 - 12:30 Sordi: Asymmetric Investment Functions and Limit Cycles: The Multiplier-

Accelerator Interaction 'Continuously' Revisited 12:30 - 14:00 LUNCH BREAK 14:00 - 16:00 SKIBA 2 (Chair: Wagener) - Kleiner Festsaal 14:00 - 14:30 Gavrila, Feichtinger, Tragler: The existence of DNS curves 14:30 - 15:00 Haunschmied, Hartl, Kort, Feichtinger: A DNS curve separating a steady

state and a limit cycle in a technology investment decision model 15:00 - 15:30 Tragler: DNS-Thresholds in a One-State Three-Control Model of the U.S.

Cocaine Epidemic 15:30 - 16:00 Kort, Caulkins, Feichtinger, Hartl: Explaining Fashion Cycles: a Skiba Curve

Analysis

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14:00 - 16:00 THEORY OF DG (Chair: Engwerda) - Ludwig-Urban-Saal 14:00 - 14:30 Rincón-Zapatero: Sufficient Conditions for Discontinuous Markov Perfect

Nash Equilibrium 14:30 - 15:00 Wirl: Markov Strategies, Patching, Inada Conditions: Uniqueness and

Indeterminacy 15:00 - 15:30 Rubio: On the Coincidence of the Feedback Nash and Stackelberg Equilibria in

Economic Applications of Differential Games 15:30 - 16:00 Oyama, Hofbauer, Takahashi: Monotone Methods for Equilibrium Selection

under Perfect Foresight Dynamics 14:00 - 16:00 REAL AND FINANCIAL MACRODYNAMICS (Chair: Flaschel) - Arthur-Krupp-Saal 14:00 - 14:30 Asada: A Two-regional Model of Business Cycles with Fixed Exchange Rates 14:30 - 15:00 Flaschel, Semmler: Currency crisis, financial crisis and large output loss 15:00 - 15:30 Semmler, Grüne: Imperfect Capital Markets, Heterogeneous Firms and Asset

Pricing 16:30 - 18:30 DYNAMIC GAMES (Chair: Puu) - Kleiner Festsaal 16:30 - 17:00 Puu: Complex Oligopoly Models by Tords Palander and Abraham Wald - Two

Little Known Contributions from 1936 17:00 - 17:30 Lorenz, Pasche: Is it reasonable to optimize? 17:30 - 18:00 Kopel, Bischi, Szidarovszky: Multiagent fishery models 18:00 - 18:30 Matsumoto, Suzuki: Profitable Chaos in Nonlinear Duopoly Market 16:30 - 18:30 INCENTIVES IN DG (Chair: El Ouardighi) - Ludwig-Urban-Saal 16:30 - 17:00 Tidball, Jean-Marie: Conjectures and Incentives in Dynamic Models 17:00 - 17:30 Kitti, Ehtamo: Adjustment of an Affine Incentive with Fixed-Point Iteration 16:30 - 18:30 MACROECONOMICS: GROWTH (Chair: Neck) - Arthur-Krupp-Saal 16:30 - 17:00 Greiner: Effects of global warming on economic growth 17:00 - 17:30 Aseev, Kryazhimskii: The Pontryagin Maximum Principle for Optimal

Economic Growth Problems

20:00 RECEPTION IN THE CITY HALL

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Thursday, May 15, 2003 09:00 - 10:30 SEMIPLENARY TALK (Chair: Rieder) - Kleiner Festsaal 09:00 - 09:45 Dockner, Nishimura: Dynamic Portfolio Management 09:45 - 10:30 Maurer: Numerical solution of some complex optimal control problems in

economic processes 09:00 - 10:30 SEMIPLENARY TALK (Chair: Kopel) - Ludwig-Urban-Saal 09:00 - 09:45 Rosser: The Rise and Fall of Catastrophe Theory Applications in Economics:

Was the Baby Thrown Out with the Bathwater? 09:45 - 10:30 Mosekilde, Laugesen: Border-Collision Bifurcations from Human Decision

Making Behavior 10:30 - 11:00 COFFEE BREAK 11:00 - 12:30 ENVIRONMENTAL GAMES (Chair: Wirl) - Kleiner Festsaal 11:00 - 11:30 García, Escudero, Martín-Herrán: An interregional Differential Game on

Pollution and Trade. Is it possible a self-enforcing agreement 11:30 - 12:00 Martin-Herran, Jorgensen, Zaccour: Agreeability and Time-Consistency in

Linear-State Differential Games 11:00 - 12:30 STOCHASTIC FINANCE (Chair: Dockner) - Ludwig-Urban-Saal 11:00 - 11:30 Tapiero: VaR Sensitive Buy-Hold-Sell Strategies 12:00 - 12:30 Cerqueti: A model for the external financing of a firm 11:00 - 12:30 LEARNING 1 (Chair: Gaunersdorfer) - Arthur-Krupp-Saal 11:00 - 11:30 Hommes, Sorger, Wagener: Stochastic Consistent Expectations Equilibria 11:30 - 12:00 Hofbauer: Index and asymptotic stability of Nash equilibria 12:00 - 12:30 Tuinstra, Wagener: On Learning Equilibria 14:00 - 16:00 DYNAMIC GAMES OF FIRMS (Chair: Zaccour) - Kleiner Festsaal 14:00 - 14:30 El Ouardighi, Bowon: Supplier and Manufacturer Collaboration on New

Product Development 14:30 - 15:00 Jorgensen, Dockner, Kort: accumulation of intellectual capital under

uncertainty 15:00 - 15:30 Petit, Sanna Randaccio: Localized spillovers and international expansion: a

dynamic analysis 15:30 - 16:00 Palokangas: Labour Market Regulation, Productivity-Improving R&D and

Endogenous Growth 16:00 - 16:30 COFFEE BREAK

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14:00 - 16:00 APPLICATIONS OF OC (Chair: Leung) - Ludwig-Urban-Saal 14:00 - 14:30 Leung: Uncertain Lifetime and Wealth Depletion 14:30 - 15:00 Elhafsi, Dodin, Elimam: Assignment and Dynamic Loading of Chemical

Products to Tankers' Compartments 15:00 - 15:30 Steindl: Optimal deployment of a dumbell satellite with tension control 14:00 - 16:00 ENDOGENOUS GROWTH (Chair: Greiner) - Arthur-Krupp-Saal 14:00 - 14:30 Brito, Venditti: Global indeterminacy in two-sector models of endogenous

growth 14:30 - 15:00 Bruha: Fiscal Policy and Multiple Equilibria in a Dynamic General Equilibrium 15:00 - 15:30 Kaas: Endogenous financial development and growth 16:30 - 18:30 STOCHASTIC GAMES (Chair: Petit) - Kleiner Festsaal 16:30 - 17:00 Yeung, Petrosyan: Agreeable Solutions in Cooperative Stochastic Differential

Games 17:00 - 17:30 Bayraktar, Poor: Equilibria in Stochastic Differential Games with Fractal

Modulation 17:30 - 18:00 Engwerda: Linear Quadratic Differential Games: an overview and its use in

macro-economic policy modeling. 16:30 - 18:30 MARKETING (Chair: Jorgensen) - Ludwig-Urban-Saal 16:30 - 17:00 Zaccour, Jorgensen, Taboubi: Incentives for Retailer Promotion in a

Marketing Channel 17:00 - 17:30 Dockner, Fruchter: Dynamic Competitive Pricing and Speed of Diffusion 17:30 - 18:00 Benchekroun: Promotion and Advertising: Complements or Substitutes? 18:00 - 18:30 Buratto, Grosset: A stochastic linear quadratic model for an advertising

campaign 16:30 - 18:30 LABOUR ECONOMICS (Chair: Kubin) - Arthur-Krupp-Saal 16:30 - 17:00 Kubin, Commendatore: The dynamics of wages and employment in a model

of monopolistic competition and efficient bargaining 17:00 - 17:30 Lang: The dynamics of french unemployment: interpretation and empirical

application in terms of strong hysteresis 17:30 - 18:00 Weinrich, Colombo: Unemployment and Inventories in the Business Cycle

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Friday, May 16, 2003 09:00 - 10:30 RENEWABLE RESOURCE MANAGEMENT (Chair: Katayama) - Kleiner Festsaal 09:00 - 09:30 Hernández, León, León: The Effect of Long-Short Distance to Consumer

Centers in the Optimization of Aquaculture Management 09:30 - 10:00 Erdlenbruch, Tidball: Sustainable forest policies - an optimal control model 09:00 - 10:30 VINTAGE MODELS 1 (Chair: Veliov) - Ludwig-Urban-Saal 09:00 - 09:30 Faggian: Applications of Dynamic Programming to Economic Problems with

Vintage 09:30 - 10:00 Fürnkranz, Feichtinger, Veliov: Age-Structured Optimal Control in Population

Economics 09:00 - 10:30 FINANCIAL MARKETS (Chair: Kort) - Arthur-Krupp-Saal 09:00 - 09:30 Bischi, Gardini, Gallegati, Leombruni, Palestrini: Herd Behavior and Price

Fluctuations in Financial Markets 09:30 - 10:00 Westerhoff: Multi-Asset Market Dynamics 10:00 - 10:30 Wieland, Westerhoff: Exchange Rate Dynamics, Central Bank Interventions

and Chaos Control Methods 10:30 - 11:00 COFFEE BREAK 11:00 - 12:30 RESOURCE MODELS (Chair: Yeung) - Kleiner Festsaal 11:00 - 11:30 Katayama, Benchekroun, Van Long: Capital Resource Substitution,

Overshooting, and Sustainable Development 11:30 - 12:00 Koulovatianos: Of Whales and Men 12:00 - 12:30 Lamantia, Bischi, Sbragia: Competition and cooperation in natural resources

exploitation 11:00 - 12:30 VINTAGE MODELS 2 (Chair: Brito) - Ludwig-Urban-Saal 11:00 - 11:30 Tsachev, Feichtinger, Veliov: Optimization of Age- and Duration-Structured

Systems: Application to Prevention and Treatment of HIV 11:30 - 12:00 Veliov: On the Role of Heterogeneity in Problems of Control of Infectious

Diseases 11:00 - 12:30 FINANCIAL MARKETS & MONEY (Chair: Bischi) - Arthur-Krupp-Saal 11:00 - 11:30 Dieci, Chiarella, Gardini: Asset price and wealth dynamics in a financial

market with heterogeneous agents 11:30 - 12:00 Manolova, Lai Tong, Deissenberg: Money and exchange in an economy with

spatially differentiated agents 12:30 - 14:00 LUNCH BREAK

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14:00 - 16:00 LEARNING 2 (Chair: Hommes) - Kleiner Festsaal 14:00 - 14:30 Arifovic, McKelvey: Implementation of the Turing Tournament 14:30 - 15:00 Colombo: Technology Adoption with Production Externalities 15:00 - 15:30 Salzano: How to approach economic complexity: from agents to systems 15:30 - 16:00 Cellarier: Learning Equilibria in a Productive Economy 14:00 - 16:00 NONLINEAR DYNAMICAL SYSTEMS (Chair: Deissenberg) - Ludwig-Urban-Saal 14:00 - 14:30 Faggini: Control of Non linear Economics Systems 14:30 - 15:00 Yegorov: Urbanization and Demographic Transition 15:00 - 15:30 van der Hoog: A Moving Horizon Approach to Disequilibrium Dynamics 15:30 - 16:00 Onozaki: A New Light on Cournot Duopoly with Differentiated Products 16:00 - 16:30 COFFEE BREAK 16:30 - 18:20 PLENARY TALK (Chair: Feichtinger) - Kleiner Festsaal 16:30 - 17:25 Rieder: Stochastic optimal control with applications to investment problems 17:25 - 18:20 Gozzi, Monte, Tessitor: Optimal investments with vintage capital. An approach

via optimal control of PDE's 18:20 - 18:30 CLOSING ADDRESS - KLEINER FESTSAAL 19:00 RECEPTION IN THE UNIVERSITY OF VIENNA (ARKADENHOF)

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Abstracts COORDINATION IN AN ABSTRACT ADAPTIVE ECONOMY Richard H. DAY, University of Southern California, Department of Economics Plenary Talk, Wed. 14.5., 9:30 - 10:30 Imperfect and incomplete information, fallible cognition and limited computing power imply that strategic economic plans are imperfectly conceived. Intended actions are, therefore, seldom if ever completely consistent. This implies that every decentralized economy must possess mechanisms that guarantee existence out of equilibrium. A sufficient set of attributes that solves this viability problem is suggested that solve this viability problem. USING DYNAMIC PROGRAMMING WITH ADAPTIVE GRID SCHEME FOR OPTIMAL CONTROL PROBLEMS IN ECONOMICS Willi SEMMLER, Universität Bielefeld, Lehrstuhl für quantitative Wirtschaftspolitik Lars GRÜNE Skiba 1, Wed. 14.5., 11:00 - 11:30 The study of the solutions of dynamic models with optimising agents have often been limited by a lack of available analytical techniques to explicitly find the global solution paths. On the other hand the application of numerical techniques such as dynamic programming (DP) to find the solution in interesting regions of the state state was restricted by the use of fixed grid size techniques. Following Grüne (1997) in this paper an adaptive grid scheme is used for finding the global solutions of discrete time Hamilton-Jacobi-Bellman (HJB) equations. Local error estimates are established and an adapting iteration for the discretization of the state space is developed. The advantage of the use of adaptive grid scheme is demonstrated by computing the solution paths of one and two dimensional economic models which exhibit complicated dynamics due to multiple equilibria, thresholds (Skiba sets) separating domains of attraction and periodic solutions. The studied examples are from economic growth, investment theory, environmental and resource economics. ON THE EFFICIENCY-EFFECTS OF PRIVATE (DIS-)TRUST IN THE GOVERNMENT Herbert DAWID, Department of Economics, University of Bielefeld Christophe DEISSENBERG, GREQAM Skiba 1, Wed. 14.5., 11:30 - 12:00 We consider a continuous-time version of the seminal Barro-Gordon model, assuming now an heterogenous private sector. In each period, a fraction of the private agents believe the policy announcements made by the government. The rest of the agents act as fully rational, fully informed players. The fraction of agents that believe the government changes over time, depending upon the difference between the payoffs they obtain and the payoffs realized by the non-believers. The government maximizes its cumulated payoff through its choice of policy announcement and realized policy. We show that the economy can have two stable equilibria. At one of these, all agents act rationally. At the other equilibrium, which is associated with a higher average utility of the private sector, a positive percentage of the agents trusts the government. The two equilibria are separated by a Skiba point associated with an unstable spiral of the canonical system.

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SKIBA REGIONS AND HETEROCLINIC BIFURCATIONS Florian WAGENER, CeNDEF, Universiteit van Amsterdam Skiba 1, Wed. 14.5., 12:00 - 12:30 The existence of Skiba points in an optimal control problem is a global qualitative property. If the problem depends on parameters, it is to be expected that the parameter region for which Skiba points can occur is bounded by global bifurcation curves. This intuitive expectation holds true. Numerical techniques have to be applied to compute such curves for particular applications. A DIRECT METHOD OF OPTIMIZATION AND ITS APPLICATION TO A CLASS OF DIFFERENTIAL GAMES George LEITMANN, College of Engineering, University of california, Optimal Control Theory, Wed. 14.5., 11:00 - 11:30 Many problems in economics and engineering can be posed as dynamic optimization problems. These problems are usually addressed via the calculus of variations or the Maximum Principle of optimal control. These methods, yielding necessary conditions for optimality, are variational in nature since they are based on comparison of solutions in a neighborhood of an optimal one. A different approach, proposed in the 1960's and recently expanded, is directed towards obtaining optimal solutions directly, that is without the use of comparison techniques. Here it is illustrated by application to a class of open-loop differential games. THE NOETHER PRINCIPLE OF OPTIMAL CONTROL Delfim F. M. TORRES, University of Aveiro, Department of Mathematics Optimal Control Theory, Wed. 14.5., 11:30 - 12:00 The relation between symmetry, conserved quantities, reduction, and minimization is well known in the context of the Calculus of Variations. Such relation plays a prominent role in modern Physics and Economics, where Emmy Noether celebrated theorems establishes conservation laws with rich interpretations (e.g. conservation of energy; the income/wealth law). We provide new versions of Noether's Principle for the Optimal Control setting, relating the invariance properties of the optimal control problems with the existence of preserved quantities along the Pontryagin extremals. Extensions include: (i) multi-parameter families of invariance transformations which may depend on time, state and control variables; (ii) Lagrangian invariance up to addition of gauge terms nonlinear on the parameters; (iii) quasi-invariant and not necessarily invariant optimal control problems. The results consider both normal and abnormal extremals. Conditions for obtaining the quasi-invariance transformations and for characterizing problems possessing given conservation laws are obtained. Examples for which one is able to find new conservation laws and new necessary optimality conditions are provided.

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TRADEOFFS OF AUSTRIAN BUDGETARY POLICIES: AN OPTIMUM CONTROL ANALYSIS Reinhard NECK, Department of Economics, University of Klagenfurt Harald STIEBER Macroeconomics, Wed. 14.5., 11:00 - 11:30 Optimum control methods have been used in various studies to determine optimal intertemporal decisions for many problems in economics and operations research. For a comprehensive survey, see, e.g., Feichtinger and Hartl (1986). For actual problems of policy-making at the macroeconomic level, however, an analytical approach has only limited relevance, because these problems are usually characterized by a great number of constraints as embodied in a model of medium or large size. Moreover, when optimal policies for macroeconomic decision problems have to be determined, uncertainty about policy effects has to be taken into account. Stochastic optimum control theory has not provided analytical solutions so far, except for very small problems. Therefore, numerical methods of dynamic optimization under uncertainty are the only means to solve problems of actual macroeconomic policy-making. In this paper, we use an algorithm for determining optimal policies for nonlinear stochastic dynamic models to deal with the problem of designing optimal budgetary policies for Austria. This issue is of great political relevance, as can be seen from recent highly controversial policy debates in this country. We choose an approach of quantitative economic policy to determine numerically optimal budgetary policies for the next few years by minimizing an intertemporal objective function subject to the constraints given by an econometric model. This model, called FINPOL4, is a medium-size macroeconometric model for Austria, relating policy and exogenous variables to objective variables of Austrian economic policies. The objective function penalizes deviations of objective variables from their desired ("ideal") values. Exogenous variables of the model are forecast over the planning horizon, which is assumed to be 2002 to 2006, using time series methods. Optimal fiscal policies are calculated over this time horizon using the stochastic optimum control algorithm OPTCON. It is shown that optimal policies can improve on the performance of the Austrian economy as compared to a simulation using extrapolated values of budgetary policy variables. A MACROECONOMIC POLICY GAME IN A MONETARY UNION Reinhard NECK, Department of Economics, University of Klagenfurt Doris BEHRENS Macroeconomics, Wed. 14.5., 11:30 - 12:00 This paper develops a dynamic game model to study strategic interactions between the decision-makers in a monetary union. In such a union, governments of the participation countries pursue national goal when deciding on fiscal policies, whereas the common central bank’s monetary policy aims at union-wide objective variables. Considering the example of a negative demand shock, we show how different solution concepts for the dynamic game between the common central bank and the national governments can be used as models of a conflict between national and supra-national institutions (noncooperative Nash equilibrium) and of coordinated policy-making (cooperative Pareto solutions).

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ASYMMETRIC INVESTMENT FUNCTIONS AND LIMIT CYCLES: THE MULTIPLIER-ACCELERATOR INTERACTION 'CONTINUOUSLY' REVISITED Serena SORDI, Dipartimento di Economia Politica, Università di Siena Macroeconomics, Wed. 14.5., 12:00 - 12:30 We study different versions of a multiplier-accelerator-type model and investigate for each of them the conditions for limit cycles. The starting point is the contribution by Sasakura (JEDC, 1996), where the author provided conditions for the existence of a unique stable limit cycle in Goodwin's (1951) model for the case of an asymmetric investment function. The matter is investigated further both for the general case and for the two particular (extreme) cases in which either only the "ceiling" or only the "floor" to investment spending is in operation. This allows us to qualify and explain Sasakura's contention that, although Goodwin attached importance to the "ceiling", the limit cycle in the model is generated without it. As a result of our analysis, Sasakura's contention appears fairly obvious if not in part misleading. A mathematical appendix at the end of the paper introduces the reader to the required 'theoretical technology', namely the Lord Rayleigh equation, its generalization to the so-called Lord Rayleigh-type equation and the distinction, due to the physicist Le Corbeiller, between two- and four-stroke oscillators. THE EXISTENCE OF DNS CURVES Caius GAVRILA, Dipartimento di Matematica, Universita degli Studi di Roma "Tor Vergata" Gustav FEICHTINGER, Vienna University of Technology Gernot TRAGLER, Vienna University of Technology Skiba 2, Wed. 14.5., 14:00 - 14:30 Recently Wagener (F.O.O. Wagener, Skiba points and the heteroclinic bifurcations, with applications to the shallow lake system, CeNDEF Working Paper, University of Amsterdam, 2002) has investigated the occurrence of Dechert-Nishimura-Skiba (DNS) points in a quite general class of one state, one co-state control systems. For systems with small discount rates, a local criterion is given for the existence of a DNS point, i.e. an initial state where the control problem has two different optimal solutions. Similarly, we consider a class of two state, two co-states control systems and analyze the existence of the DNS curves, i.e. the 1-dimensional topological manifolds of the DNS points in the states plane. The analysis is applied to an optimal control model of the methadone maintenance treatment for a population of injection drug users. A DNS CURVE SEPARATING A STEADY STATE AND A LIMIT CYCLE IN A TECHNOLOGY INVESTMENT DECISION MODEL Josef L. HAUNSCHMIED, Vienna Univ. of Technology, Department of OR and Systems Theory Richard HARTL, University of Vienna Peter KORT, Tilburg University Gustav FEICHTINGER, Vienna University of Technology Skiba 2, Wed. 14.5., 14:30 - 15:00 Technology advances quickly these days. Therefore, in order to keep up with its economic environment a firm should respond to new technological developments. Otherwise , its products become old-fashioned and customers will tend to go to competitors. We establish the optimal technology investment decision within a dynamic model, in which the baseline technology level rises over time. The problem is analyzed by designing a two state variable optimal control model. It turns out that in the state space a DNS-(Dechert-Nishimura-Skiba) curve can be determined that separates different long run outcomes, viz., zero investment on the one hand and constant (positive) investment and/or a cyclical sequence of zero and positive investment on the other hand.

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DNS-THRESHOLDS IN A ONE-STATE THREE-CONTROL MODEL OF THE U.S. COCAINE EPIDEMIC Gernot TRAGLER, Vienna University of Technology, Inst. f. Econometrics, OR & Systems Theory Skiba 2, Wed. 14.5., 15:00 - 15:30 This presentation focuses on a one-state optimal control model of drug use, which is empirically validated with data from the current U.S. cocaine epidemic. The state variable represents the number of cocaine users. The model has three control variables, i.e. spending for primary prevention, treatment, and price-raising law enforcement, respectively. The objective is to find the optimal mix of the three controls, which minimises the discounted stream of the sum of social costs of cocaine use and total control spending. It is shown that for wide ranges of parameter values a DNS-threshold may occur, separating the basins of attraction of two long-run steady states. Below the threshold, the optimal policy leads to a low number of users, but demands high levels of spending (“eradication policy”). Above the threshold, convergence is to a relatively high number of users, but with lower levels of spending (“moderation policy”). A sensitivity analysis is presented to demonstrate the effect of certain parameter changes on the DNS-threshold. Moreover, it is shown that the introduction of a budget constraint may lead to a second threshold above the high steady state, separating this one from an even higher, third steady state which is a boundary equilibrium generated by the budget constraint. Interestingly, the introduction of a budget constraint may also have a completely opposite effect, i.e., it may cause DNS-thresholds to disappear. EXPLAINING FASHION CYCLES: A SKIBA CURVE ANALYSIS Peter KORT, Department of Econometrics & Operations Research, Tilburg University Jonathan P. CAULKINS, Carnegie Mellon University Gustav FEICHTINGER, Vienna University of Technology Richard F. HARTL, University of Vienna Skiba 2, Wed. 14.5., 15:30 - 16:00 This paper considers the problem of a fashion trend-setter that has to deal with an imitator, while the imitator is able to produce the same product against a lower cost. A one dimensional product space is considered, which is an abstraction of the key attribute of some consumer good. An obvious example is the width of neckties (which we all have observed to vary over time). The design houses define what is fashionable, while off label brands imitate them. The decision maker's state variable denotes the position in the one dimensional product space. The imitator always chases this position, because its corporate strategy is simply to imitate the market leader. Hence, this is an optimal control problem, not a dynamic game, where the second state variable is the imitator's position in the product space. It turns out that the investment cost of making new designs and the initial position of both firms in the product space are crucial for the structure of the optimal solution. For low costs it is optimal to cycle around the product space, while a Skiba curve separates the two possible directions of changing a design initially. For intermediate values of the cost, two other Skiba curves circumvent an area around the middle of the product space where it is optimal for the decision maker not to move. Then the imitator simply catches up and conquers the whole market. If the investment cost of making new designs is large, two other Skiba curves arise, which separate a policy of "not changing the design" from a policy where the market leader makes an initial major change of the design after which the design is not changed anymore.

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SUFFICIENT CONDITIONS FOR DISCONTINUOUS MARKOV PERFECT NASH EQUILIBRIUM Juan Pablo RINCÓN-ZAPATERO, Universidad de Valladolid, Dpto. Economía Aplicada (Matemáticas) Theory of DG, Wed. 14.5., 14:00 - 14:30 In this paper we deal with the analysis of piecewise smooth Markov perfect Nash equilibrium in finite horizon differential games. We establish sufficient conditions of optimality that seems to be new in the literature and apply them to a class of resource games. The results are based in the new approach recently developed by this author and collaborators to study non-cooperative differential games. Hence, the type of games analyzed is such that there is no constraints on the control variables and the dimension of the state space is lesser or equal than the dimension of the control space of each player. MARKOV STRATEGIES, PATCHING, INADA CONDITIONS: UNIQUENESS AND INDETERMINACY Franz WIRL, University of Vienna, Theory of DG, Wed. 14.5., 14:30 - 15:00 Multiple Nash equilibria in Markov strategies that are observed in dynamic games can be classified into: (i) a `saddlepoint' equilibrium that is globally defined; (ii) a family of solution curves which are typically of local character and thus require patching to obtain global strategies. It is shown that these two types of equilibria relate to the increasing (i) and the decreasing part (ii) of an initial manifold. While intuition suggests that Inada conditions ensures uniqueness due to the implicit requirement of global strategies, the following is found: If the elasticity of marginal utility is (everywhere) greater than (n-1)/n (and thus in particular if greater than 1), then the Nash equilibrium is unique. The opposite inequality, elasticity of marginal utility is globally less than (n-1)/n implies that no sadlepoint equilibrium exists, and all (negative) initial conditions determine a corresponding equilibrium, which is the maximum of conceivable indeterminacy. ON THE COINCIDENCE OF THE FEEDBACK NASH AND STACKELBERG EQUILIBRIA IN ECONOMIC APPLICATIONS OF DIFFERENTIAL GAMES Santiago RUBIO, Department of Economic Analysis, University of Valencia Theory of DG, Wed. 14.5., 15:00 - 15:30 In this paper the scope of the applicability of the Stackelberg equilibrium concept in differential games is investigated. Firstly, it is showed that for a class of differential games with state-interdependence the stationary feedback Nash equilibrium coincides with the stationary feedback Stackelberg equilibrium independently of the player being the leader of the game. Secondly, sufficient conditions for obtaining the coincidence between the two equilibria are defined. A review of different economic models shows that this coincidence is going to occur for a good number of economic applications of differential games. This result appears because of the continuous-time setting in which differential games are defined. In this setting the first movement advantage of the leader may disappear and then both equilibria coincide.

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MONOTONE METHODS FOR EQUILIBRIUM SELECTION UNDER PERFECT FORESIGHT DYNAMICS Daisuke OYAMA, University of Vienna, Department of Economics Josef HOFBAUER, Universität Wien Satoru TAKAHASHI Theory of DG, Wed. 14.5., 15:30 - 16:00 The paper studies equilibrium selection in supermodular games based on a class of perfect foresight dynamics, introduced by Matsui and Matsuyama (JET 1995) and further developed by Hofbauer and Sorger (JET 1999, IGTR 2002) and Oyama (JET 2002). A normal form game is played repeatedly in a large society of rational agents. There are frictions: opportunities to revise actions follow independent Poisson processes. Each agent forms his belief about the future evolution of action distribution in the society to take an action that maximizes his expected discounted payoff. A perfect foresight path is defined to be a feasible path of action distribution to which every agent at revision opportunity takes a best response. A Nash equilibrium is said to be globally accessible if for each initial condition, there exists a perfect foresight path converging to this equilibrium; a Nash equilibrium is said to be absorbing if there exists no perfect foresight path escaping from a neighborhood of this equilibrium. By appealing to the monotonicity of the correspondence whose fixed points are perfect foresight paths, a unique Nash equilibrium that is absorbing and globally accessible for small frictions is identified for certain classes of supermodular games. Our equilibrium selection results are compared with those obtained via different approaches. A TWO-REGIONAL MODEL OF BUSINESS CYCLES WITH FIXED EXCHANGE RATES Toichiro ASADA, Faculty of Economics, Chuo University Real and Financial Macrodynamics (Flaschel), Wed. 14.5., 14:00 - 14:30 In this paper, we investigate a nonlinear macrodynamic model of business cycles which describes the dynamic interaction of two regions which are connected through inter-regional trade and inter-regional capital movement with fixed exchange rates. Our model is formulated as a five-dimensional system of nonlinear differential equations, which is a two-regional extension of the Kaldorian business cycle model. We study the local stability / instability and the condition for the existence of the cyclical fluctuation analytically, and we also present some numerical examples which support our analytical results. CURRENCY CRISIS, FINANCIAL CRISIS AND LARGE OUTPUT LOSS Peter FLASCHEL, Universität Bielefeld, Fakultät für Wirtschaftswissenschaften Willi SEMMLER, Universität Bielefeld Real and Financial Macrodynamics (Flaschel), Wed. 14.5., 14:30 - 15:00 Given the volatility (or in the case of fixed exchange rates: vulnerability) of exchange rate systems there is a reemergence of interest in the effects of such occurences, in particular large currency shocks, and their impact on domestic financial markets and the output of firms. We use a dynamic portfolio approach to asset markets to model the forces that establish such currency crisis, and the resulting large exchange rate shocks, on asset allocation, investment and output in a small open economy, as for example Thailand. Given such contemporary economies, where a large fraction of debt is denominated in foreign currencies, for example in dollars, exchange rate shocks have a strong impact on liabilities of households, firms, banks and governments. Following a model sketched by Krugman (1999, 2001) we show rigorously in a nonlinear dynamic Mundell-Fleming-Tobin type model how large currency depreciations can come about and that such large currency shocks set in motion financial market, investment and output reactions that can, due to the existence of strong nonlinearities in goods market behavior and thus multiple equilibria, lead to low level real equilibria and thus large output losses.

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IMPERFECT CAPITAL MARKETS, HETEROGENEOUS FIRMS AND ASSET PRICING Willi SEMMLER, Universität Bielefeld, Lehrstuhl für quantitative Wirtschaftspolitik Lars GRÜNE Real and Financial Macrodynamics (Flaschel), Wed. 14.5., 15:00 - 15:30 We consider heterogeneous firms that maximize their present value through a dynamic investment strategy. Although firms behave the same, they are heterogeneous with respect to their size. They face imperfect capital markets and their credit conditions may depend on their size. We then explore to what extent debt constraints and endogenous credit cost, due to collateralized borrowing, affect the present value of firms. In our model the dynamic decision problem of maximizing the present value of firms is separated from consumption decisions. Yet, we can treat the present value of firms as constraint on consumption. We solve for the present value and thus of the asset price of heterogeneous firms by the use of a dynamic programming algorithm with exible grid size. We want to thank Jess Benhabib, John Donaldson, Martin Lettau and Michael Woodford for helpful discussions and comments. We also want to thank participants in a workshop at the University of Technology, Vienna, the Macroeconomic Workshop at Columbia University, and the SCE conference, at Yale University, June 2001, and participants of the workshop on Economic Dynamics in Leiden, June 2002.

COMPLEX OLIGOPOLY MODELS BY TORDS PALANDER AND ABRAHAM WALD - TWO LITTLE KNOWN CONTRIBUTIONS FROM 1936 Tönu PUU, Umeå University, CERUM Dynamic Games, Wed. 14.5., 16:30 - 17:00 In 1936 two outstanding economists, Tord Palander from Sweden, then visiting scholar at the Cowles Commission, and Abraham Wald in Vienna, independently presented very similar duopoly models. Both took their departure in the Joan Robinson case, where the demand curve has an inward kink due to different demand elsticities in sub-markets. As demonstrated in elementary textbooks, the marginal revenue curve then jumps up, and the monopolist may have two different local profit maxima. Palander and Wald set out to apply this to Cournot duopoly. In that case it may be appropriate for one competitor to choose different local optima, depending on the supply of the other. As a consequence, the reaction functions may become non-monotonic, including jumps, and there may be several coexistent Nash equilibria, or none at all. Palander gave a detailed analysis of the fragmented basins for coexistent equilibria, or oscillations. It is also quite easy to make these models produce chaotic motion by very slight modifications.

IS IT REASONABLE TO OPTIMIZE? Hans-Walter LORENZ, Department of Economics, University of Jena Markus PASCHE, Friedrich-Schiller-Universität Jena Dynamic Games, Wed. 14.5., 17:00 - 17:30 Models of bounded rationality assume that real choice behavior can be characterized by heuristics, rules of thumb, or routines rather than by solving an optimization calculus. In a strategic context fully rational choice behavior leads to the Nash equilibrium as a natural solution concept. However, even simple heuristic rules may depend on expectations regarding the choices of other players. If players are committed to their type of choice behavior, a broader class of equilibria can be established. Usually, different types of choice behavior perform differently. Hence it is reasonable to assume that a competitive selection process rules out inferior behavioral types. As a result, an equil. profile of types is characterized by the property that no player can achieve a better performance by commiting to another type. It can then be shown that in such an equil. profile the fully rational optim. behavior need not be the unique type. Moreover, in some cases optimizing behavior might completely be ruled out. The concept is applied to the one-shot PD game. In an environment where players are randomly matched to play the PD game distributions of types can be derived under which cooperative behavior can be observed.

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MULTIAGENT FISHERY MODELS Michael KOPEL, University of Technology, Dept of Managerial Econ and IO Gian Italo BISCHI, University of Urbino Ferenc SZIDAROVSZKY Dynamic Games, Wed. 14.5., 17:30 - 18:00 Following Szidarovszky and Okuguchi (1998) we propose an oligopoly model where n players sell the harvested fish in m markets. Moreover, we assume that agents do not have perfect knowledge of the fish stock. This differs from the current approach in resource economics literature, where it is usually assumed that fishermen, when they decide their optimal harvesting, have precise knowledge of the environment. Instead, we think that in the real world this will hardly be the case. More realistically, these economic agents have access to a collection of past data about the harvested amounts of fish and some other indicators of the size of the fish population, from which they try to derive an estimate of the future fish stock. With every new piece of information, their estimate will be updated and used to determine the future harvesting activities. In our model we assume a simple learning rule called adaptive expectations: at the end of each period, using past observations about harvests and fish stock, fishermen are able to derive the exact stock of the resource, and then they make a prediction about the future fish stock by forming a weighted average between the current fish stock and their previous prediction. We consider two different models: in the first one we assume that each player maximizes his own expected profit, as in a typical non cooperative oligopolistic competition; in the second one we assume that the players form a cooperative venture, where each player determines its harvesting activity such that the joint profit of all players is maximized. We compare the Nash equilibria obtained in these two cases, and we examine their stability properties under the assumption that the game is played repeatedly by boundedly rational players (due to the limited knowledge of the fish stock and the related adaptive learning process). The results obtained confirm that cooperation does not only lead to higher conservation, but the larger stock eventually leads also to a higher total harvest (due to increased growth of the resource) like in the above mentioned prisoner’s dilemma. However, unexpected results are obtained about the global dynamic properties. In fact, from the point of view of the mathematical structure of the dynamic model, when we replace the assumption of fishermen with perfect foresight about the next period fish stock by the weaker assumption of adaptive expectations, a one-dimensional dynamical system is replaced by a two-dimensional one, and this implies that remarkable differences may arise concerning the role of the initial conditions, due to more complex structures of the basins of attraction and to the occurrence of global bifurcations which change their topological properties. The results obtained are characterized by complex dynamic patterns and bifurcation phenomena, because the interactions of human economic decision making with ecological dynamics are highly non linear (on this point see also Rosser, 2001). Moreover, in our model the complexity of the basins of attraction is related to the fact that the dynamic evolution of the game is obtaioned through the repeated application of a two-dimensional noninvertible map. The main problems addressed in our work are : (i) the influence of the market structure and the role of strategic effects on the evolution of the biomass in an oligopoly framwork, both in the non cooperative and in the cooperative case; (ii) the role of harvesting costs in the problem of extinction or conservation of the resource; (iii) the influence of errors in predicting the fish stock when determining future harvesting activities.

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PROFITABLE CHAOS IN NONLINEAR DUOPOLY MARKET Akio MATSUMOTO, Chuo University, Department of Economics Mami SUZUKI, Aichi Gakusen University Dynamic Games, Wed. 14.5., 18:00 - 18:30 This study investigates an economic implicationof chaotic fluctuations that are observed in a nonlinear economic dynamic model. To this end, it constructs a nonlinear discrete tiem Cournot duopoly model in which firms have U-shaped or inverted U-shaped reaction functions due to productio externality and shows that chaotic output fluctuations can arise for strong nonlinarities. Two main results of this study are the following: (1) it is theoretically as well as numerically confirmed that one of the duopolists can benefit in the sense that the long-run average profit takne along a chaotic trajectory is higher than the profit taken at a equilibrium point; (2) it is verified with numerical simulations that both duopolists can benefit from chatoic trajectories if they are heterogeneou. CONJECTURES AND INCENTIVES IN DYNAMIC MODELS Mabel TIDBALL, INRA-LAMETA Institut National de Recherche, Agronomique Alain JEAN-MARIE, LIRMM - University of Montpellier 2 Incentives in DG, Wed. 14.5., 16:30 - 17:00 The most popular equilibrium concept in Economics is the Nash Equilibrium. Other concepts have been introduced in order to better observed behaviors. Another non co-operative equilibrium concept is the Conjectural Variation Equilibrium (CVE). According to this concept, each agent chooses his most favorable action taking into account that rival strategies are a conjectured function of his own strategy. Finally, in order to drive the outcome of a game towards a Pareto efficient one, the idea of Incentive Equilibrium has been proposed (Ehtamo and Hamalainen, Jorgensen and Zaccour). It turns out that Incentive Equilibrium is formally closely related to CVE. The CVE model has been the subject of much controversies. However, it turns out that the initial (static) CVE model can be justified as the steady state of a broader dynamic framework. The idea is that agents, facing incomplete information, or having limited rationality, form and revise beliefs about their opponents. For instance Friedman and Mezzetti (2002) and Jean-Marie and Tidball (2002) propose procedures by which agents adjust their conjectures in function of the opponent's play. This presentation will review the models of Friedman-Mezzetti, Jean-Marie-Tidball, and the dynamic Incentive Equilibrium models, in order to clarify the parallel between CVE and Incentive Equilibria. Moreover, we shall compare and discuss the notions of consistence of CVE and that of the Credibility of Incentive Equilibria. ADJUSTMENT OF AN AFFINE INCENTIVE WITH FIXED-POINT ITERATION Mitri KITTI, Helsinki University of Technology, Systems Analysis Laboratory Harri EHTAMO, Helsinki University of Technology Incentives in DG, Wed. 14.5., 17:00 - 17:30 We study a principal-agent game where the principal commits to an affine incentive. We suppose that the principal has incomplete information but he can adjust the incentive according to the myopically behaving agent's reactions when the game is played repeatedly. The adjustment process can be considered as a learning model. We derive convergence conditions for fixed-point iteration as an adjustment scheme and study a related continuous time process. The analysis is based on parameterizing the problem such that we obtain a degree zero homogeneous system of equations that satisfies Walras' law. Keywords: incentives, principal-agent problems, fixed-point iteration, adjustment, learning, Walras' law

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EFFECTS OF GLOBAL WARMING ON ECONOMIC GROWTH Alfred GREINER, Bielefeld University, Macroeconomics: Growth, Wed. 14.5., 16:30 - 17:00 This paper analyzes the interrelation between anthropogenic global warming and economic growth. It is assumed that deviations from the pre-industrial average global surface temperature negatively affect aggregate output and utility. The government levies a tax on output and a tax on greenhouse gases. Assuming a basic endogenous growth model the effects of varying the tax rates are analyzed as concerns economic growth, economic welfare and as concerns the rise in average global surface temperature. Using simulations, it is demonstrated that higher emission taxes may both raise economic growth and welfare while reducing the extent of global warming. In addition, situations exist where a rise in emission taxes reduces economic growth but raises welfare. This holds for both the economy on the balanced growth path and for the economy on the transition path. In the social optimum economies with cleaner technologies have fewer emissions than economies with less clean production technologies. This holds because economies with cleaner technologies invest relatively more in abatement than economies with less clean technologies. Relative means that abatement spending per gross emissions is higher. Further, the second best abatement share is computed for the descriptive version of a similar model and the corresponding growth rate. It turns out that the abatement share is the higher the more polluting the technology but, nevertheless, emissions are higher compared to economies with a less polluting technology. THE PONTRYAGIN MAXIMUM PRINCIPLE FOR OPTIMAL ECONOMIC GROWTH PROBLEMS Sergei ASEEV, International Institute for Applied Systems Analysis, A. KRYAZHIMSKII Macroeconomics: Growth, Wed. 14.5., 17:00 - 17:30 The paper is concerned with the development of first-order necessary optimality conditions for infinite horizon optimal control problems arising in the studies of economic growth processes. An approximation approach is used to obtain a set of new versions of the Pontryagin maximum principle. The developed versions of the maximum principle involve additional conditions on the adjoint variables and the Hamiltonian. In some cases these additional conditions allow one to guarantee the validity of the standard transversality conditions at infinity. The results obtained generalize some earlier results in this direction. DYNAMIC PORTFOLIO MANAGEMENT Engelbert J. DOCKNER, Department of Business, University of Vienna Kazuo NISHIMURA Semiplenary Talk, Thu. 15.5., 9:00 - 9:45 The efficient management of dynamic portfolio decisions plays a crucial role in the investment industry and is the focus of many recent theoretical as well as empirical studies. This paper presents a survey of the different methods, models and applications of dynamic investment problems. In particular, we concentrate on the dynamic programming approach pioneered by Samuelson and Merton in which one or several state variables are modelled as Ito processes and investors choose their optimal portfolios over a finite or infinite investment horizon. As an alternative, we also discuss the stochastic programming approach in which alternative return scenarios are modelled on the basis of lattice structures and optimal portfolios are derived using linear or non-linear programming techniques. We evaluate these two alternatives and discuss their applicability to different portfolio management problems. We close our presentation by focussing on two specific applications, strategic asset allocation and dynamic asset and liability management.

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NUMERICAL SOLUTION OF SOME COMPLEX OPTIMAL CONTROL PROBLEMS IN ECONOMIC PROCESSES Helmut MAURER, Westfälische Wilhelms-Universität Münster, Institut für Numerische Mathematik Semiplenary Talk, Thu. 15.5., 9:45 - 10:30 Substantial efforts have gone into the modeling of various economic processes as optimal control problems. Optimal solutions to control problems with a low state dimension and simple control constraints may eventually be obtained from a thorough discussion of the first order necessary optimality conditions: the Pontryagin maximum principle. For higher dimensional optimal control problems which are subject to possibly nonlinear control and state constraints, the maximum principle does not provide enough information to determine the structure of the optimal control, i.e., the sequence and location of arcs with active or inactive the contraints. In this talk, we present two numerical approaches that have successfully been used for solving complex optimal control problems. These methods also provide complete information on adjoint variables which is needed to check first and higher order optimality conditions. The numerical methods also allow to compute the sensitivity differentials of optimal solutions w.r.t. parameter variations in the system. We present three numerical examples to illustrate these methods: (1) A recycling model with two control variables and a mixed control-state constraint; (2) A production-inventory model with two control components where one control is of "bang-singular-bang" type; (3) Two control models of HIV with L1-type functionals where the optimal controls are shown to be bang-bang. THE RISE AND FALL OF CATASTROPHE THEORY APPLICATIONS IN ECONOMICS: WAS THE BABY THROWN OUT WITH THE BATHWATER? Barkley ROSSER, James Madison University, Program in Economics Semiplenary Talk, Thu. 15.5., 9:00 - 9:45 This paper reviews the controversy surrounding the use of catastrophe theory in economics. Applications are examined and underlying assumptions are noted. Arguments brought against the use of catastrophe theory are reviewed as are the responses to these. Modern replacements for catastrophe theory are also noted. In general the author is in sympathy with the view that the baby was thrown out with the bathwater, that the criticisms were exaggerated and economists have been unduly frightened off from using catastrophe theory, which continues to be appropriate in many cases and circumstances. BORDER-COLLISION BIFURCATIONS FROM HUMAN DECISION MAKING BEHAVIOR Erik MOSEKILDE, Department of Physics, The Technical University of Denmark Jakob LAUGESEN Semiplenary Talk, Thu. 15.5., 9:45 - 10:30 Many problems in management and behavioral science lead to piecewise-smooth dynamical systems. Human decision making behavior, for instance, often entails logical considerations such that one type of decisions are made under certain circumstances while other conditions lead to a different type of decisions. The purpose of the present talk is to discuss the bifurcation scenarios and transitions to chaos that one can observe in a two-stage production-distribution system with logical functions in the inventory control algorithm. We show how the so-called border-collision bifurcations lead to transitions that are quite different from the transitions we know from smooth dynamical systems. A periodic orbit, for instance, can bifurcate directly into a chaotic attractor, and a variety of different period-multiplication processes can take place. We also consider the transition to chaos via border-collision bifurcations on a two-dimensional torus. In this connection we show that the domains of synchronization differ qualitatively from the Arnol'd tongues known for smooth systems.

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AN INTERREGIONAL DIFFERENTIAL GAME ON POLLUTION AND TRADE. IS IT POSSIBLE A SELF-ENFORCING AGREEMENT Cabo GARCÍA, Dept. Economía Aplicada (Matemáticas), Universidad de Valladolid Elena ESCUDERO Guiomar MARTÍN-HERRÁN, GERAD and University of Valladolid Environmental Games, Thu. 15.5., 11:00 - 11:30 Most of the new environmental phenomena have an intrinsic interregional dimension due to transnational or global spillovers. The international dimension of the environment is a source of substantial interdependence among nations. The negotiating process is trying to link environmental protections and trade (as in the environment clause in GATT/WTO). This paper studies transboundary pollution control in a dynamic game model where two regions are engaged in interregional trade. A good produced in one region is traded to the other region which uses it as an input. The traded good is supplied by region A, while region B decides its production and consequently the demand for this traded good. Thus total production is fixed, and the emissions of pollutants are also determined as a by-product. Under cooperation the price and the pollution stock are lower, while both regions are better-off. Region A agrees to a lower supply while region B demands less intermediate good. This lowers the price and a cuts down production and consequently emissions. If cooperation fails because cheating is detected, players apply threat strategies under which both regions obtain less welfare. Subgame-perfect strategies are credible and consequently, a self-enforcing agreement is achieved. AGREEABILITY AND TIME-CONSISTENCY IN LINEAR-STATE DIFFERENTIAL GAMES Guiomar MARTÍN-HERRÁN, GERAD and University of Valladolid, Steffen JORGENSEN, University of Southern Denmark Georges ZACCOUR, GERAD and HEC Montreal Environmental Games, Thu. 15.5., 11:30 - 12:00 The paper identifies conditions under which time-consistency and agreeability, two intertemporal individual rationality concepts, can be verified in linear-state differential games. An illustrative example drawn from environmental economics is provided. VAR SENSITIVE BUY-HOLD-SELL STRATEGIES Charles S. TAPIERO, ESSEC, Stochastic Finance, Thu. 15.5., 11:00 - 11:30 Strategies of the type “buy-hold-sell” involve necessarily both gains and losses, appropriately balanced between what an investor is willing to gamble and how much these gambles are worth to him. Risk neutral pricing has resolved the dilemma of what utility function to use to evaluate uncertain payoffs. In practice, there may be problems in applying such an approach because markets may be incomplete and individual investors are generally risk sensitive, expressing varied preferences and use historical data. As a result, both price and risk may be associated to the decision to buy-hold or sell a financial asset. In this paper, we seek to maintain the risk neutral pricing framework and at the same time associate to an individual investor a quantile risk probability over the relevant amount of time a decision can be reached. Such an approach, also coined VaR efficiency provides a combined approach to trading based on both risk neutrality and individual risk preferences based on the well practiced VaR approach. Further, the approached followed in this paper is applicable to assets we own as well as to the exercise of options over their relevant life time. A number of examples are considered spanning Russian options, American options, Look Back options as well as simple buy, sell and hold decisions that are limited in time. A, buy-sell on trinomial random walk problem is treated analytically however.

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A MODEL FOR THE EXTERNAL FINANCING OF A FIRM Roy CERQUETI, University of Rome "La Sapienza", DIMADEFA-Facoltà di Economia Stochastic Finance, Thu. 15.5., 12:00 - 12:30 The basic idea of this work is due to a joint paper of Cifarelli, Peccati, Tagliani, Salsa and Masciandaro, and we propose a new modelling associated to the financing of a firm via legal or illegal ways. The economic problem is to choose the optimal interest rate that the financier has to apply to the firm. The mathematic tool, that we used, is the stochastic control theory. The dynamic that describes the wealth of the firm is a standard Black and Scholes Equation, conditioned to the payment of the debt. We assume that the interest rate is a stochastic control in an admissible region defined by constraints, that depend on the aim of the finacier: in the legal case the financier does not want the bankruptcy of the firm; in the illegal case the financier wants the bankruptcy of the firm, in a time as less as possible. For this second case we analyze the problem of the renegotiation of the debt, and generally we study the main properties of the model. STOCHASTIC CONSISTENT EXPECTATIONS EQUILIBRIA Cars HOMMES, University of Amsterdam, CeNDEF Gerhard SORGER Florian WAGENER, Universiteit van Amsterdam Learning 1, Thu. 15.5., 11:00 - 11:30 The notion of consistent expectations equilibrium is extended to economies that are described by a nonlinear stochastic system. Agents in the model do not know this system and use a simple linear forecasting rule to form their expectations. Along a stochastic consistent expectations equilibrium (SCEE), these expectations are correct in a linear statistical sense, i.e., the unconditional mean and autocovariances of the actual (but unknown) nonlinear stochastic process coincide with those of the linear stochastic process on which the agents base their beliefs. In general, the linear forecasts do not coincide with the true conditional expectation, but a SCEE is an `approximate rational expectations equilibrium' in the sense that forecasting errors are unbiased and uncorrelated. Sample autocorrelation learning of SCEE is studied in an overlapping generations framework. INDEX AND ASYMPTOTIC STABILITY OF NASH EQUILIBRIA Josef HOFBAUER, Institut für Mathematik, Universität Wien Learning 1, Thu. 15.5., 11:30 - 12:00 The asymptotic stability of Nash equilibria under adjustment dynamics arising from evolutionary and learning models is investigated. The connection to the index will be discussed. Potential and supermodular games play a special role.

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ON LEARNING EQUILIBRIA Jan TUINSTRA, Department of Quantitative Economics and CeNDEF, University of Amsterdam Florian WAGENER, Universiteit van Amsterdam Learning 1, Thu. 15.5., 12:00 - 12:30 We investigate an inflationary overlapping generations model where households predict inflation by running a least squares regression of inflation rates or prices on their past levels. We critically examine the results on learning equilibria, obtained by Bullard (1994) and Schoenhofer (1999) in this framework. They show that an increase in the money growth rate may lead to limit cycles and endogenous fluctuations. We suggest an alternative estimation procedure, that starts from the same perceived law of motion, but is more sensible from an econometrician's point of view. We prove that for this estimation procedure there is global convergence on the monetary steady for a large set of savings functions. We also study, in an heterogeneous agents framework, an evolutionary competition between the two estimation procedures, where the fraction of the population using a certain estimation procedure is determined by its past quadratic forecast error. We find that the more sensible estimation procedure is not always able to drive out the other estimation procedure, and endogenous fluctuations may still be observed. SUPPLIER AND MANUFACTURER COLLABORATION ON NEW PRODUCT DEVELOPMENT Fouad EL OUARDIGHI, ESSEC Business School, Kim BOWON Dynamic Games of Firms, Thu. 15.5., 14:00 - 14:30 Suppliers often collaborate with manufacturing companies on developing new products. But, there is a potential tradeoff in their endeavor. On the one hand, there needs to be a short-term collaboration between the supplier and the manufacturer on the manufacturer’s current product. For instance, in order to gain a larger market share for the existing product, it would be important for the product’s quality to improve and/or for its price to decrease. The manufacturer expects its supplier to support its efforts to improve its existing product’s value. On the other hand, the manufacturer needs its supplier’s help with developing a new product, which is necessary for the manufacturing company to continue to grow in the market. Compared with the joint efforts to improve the existing product’s quality, collaborating for new product development is of long-term endeavor. Now the fundamental issue facing the supplier and the manufacturer respectively is how to allocate its resources between improving the existing product and developing a new one. By improving the existing product, they expect to increase their 'short-term' profitability. By enhancing the chance to have a successful new product development, they can expect to earn ‘future profit,’ which is vital for their continuous growth. Since they have to allocate their ‘present’ resources between ‘current’ operations and ‘future’ possibility, they are facing a tradeoff ACCUMULATION OF INTELLECTUAL CAPITAL UNDER UNCERTAINTY Steffen JORGENSEN, University of Southern Denmark, Dept. of Organization and Management Engelbert DOCKNER, University of Vienna Peter KORT, Tilburg University Dynamic Games of Firms, Thu. 15.5., 14:30 - 15:00 The paper establishes prescriptions for the growth of a new company in the IT industry. The company is personally owned and partially financed by venture capital. Among the questions the paper addresses are: how much debt (if any) should the firm attract to help financing the development of the firm, with a particular view to making a technological breakthrough. The firm wishes to avoid bankruptcy causes by an inability to service the debt. How should a wish to grow fast by investing in intellectual capital be balanced against the owners' wish to consume? KEYWORDS: capital accumulation; investments, dividends, debt financing; stochastic optimal control

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LOCALIZED SPILLOVERS AND INTERNATIONAL EXPANSION: A DYNAMIC ANALYSIS Maria Luisa PETIT, University of Rome "La Sapienza", Francesca SANNA RANDACCIO Dynamic Games of Firms, Thu. 15.5., 15:00 - 15:30 It has been empirically shown that firms invest in foreign countries with the aim to absorb technological knowledge. However, the recent literature on technological innovation and foreign expansion has not fully taken into account these features of foreign direct investment. Introducing this new element into the analysis implies assuming that multinationals and exporters operate with different degrees of technological spillovers. Our aim is to study how these differences in the transmission of knowledge may affect the firms' incentive to innovate and their behaviour in an international market, that is their choice between serving foreign markets via exports or foreign investments. JEL: C72, L13, 032 Keywords: innovation, geographical location, international strategy, multinational enterprise.

LABOUR MARKET REGULATION, PRODUCTIVITY-IMPROVING R&D AND ENDOGENOUS GROWTH Tapio PALOKANGAS, Department of Economics, University of Helsinki Dynamic Games of Firms, Thu. 15.5., 15:30 - 16:00 We present a growth model in which R&D increases productivity, union-firm bargaining determines the distribution of rents and the government can support unions by labour market regulation. We show that if unions are intially very strong, regulation increases only the workers' profit share and has no impact on employment and growth. Otherwise, regulation increases wages. Because firms try to escape this cost increase through the improvement of productivity by R&D, the economy grows faster. Regulation (deregulation) is desirable when the growth rate is below (above) some critical level. Technically, the paper is organized as follows: (i) We construct an extensive game, where the government determines relative union bargaining power, each-union firm pair bargains over the wage and the workers' profit share, firms decide on output and research, and finally consumers decide on spending and saving. The game is solved by backward induction. (ii) We construct a deterministic optimal program for a firm which is able to invest in R&D and observes the consumers' demand function for its output. (iii) We analyse union-firm alternating offers-game in the stationary state of a firm and draw conclusions about the effects of relative union bargaining power on growth and employment.

UNCERTAIN LIFETIME AND WEALTH DEPLETION Siu Fai LEUNG, Department of Economics, Hong Kong University of Science and Technology Applications of OC, Thu. 15.5., 14:00 - 14:30 "When do borrowing constraints bind?" is a topic that has attracted a good deal of attention in both the theoretical and empirical literature in economics (see Leung (1994), Rabault (2002), and the references therein). Binding borrowing constraint occurs in different types of model. The success of these models in generating binding borrowing constraints can help explain the puzzle of the prevalence of liquidity constrained households observed in the empirical literature (Leung 2000, Rabault 2002). In this paper, I continue to study the nature of the binding borrowing constraint in Yaari's (1965) model. As shown in Leung (1994, 2000), the borrowing constraint (which is a state variable inequality constraint) in Yaari's optimal control problem must bind over a period of time that ends at the maximum lifetime. This result has important theoretical implications (Leung 2001, 2002) and significant empirical relevance (Leung 1994, 2000). Despite these contributions, there are still many questions awaiting answer. This paper attempts to address two specific questions: when does the borrowing constraint begin to bind terminally and is the terminal wealth depletion time unique? I derive some new results on the optimality and uniqueness of the terminal wealth depletion time. The analysis shows how to locate the optimal terminal wealth depletion time when the equation that determines it has multiple solutions.

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ASSIGNMENT AND DYNAMIC LOADING OF CHEMICAL PRODUCTS TO TANKERS' COMPARTMENTS Mohsen ELHAFSI, University of California, Graduate School of Management Bajis DODIN Abdelghani ELIMAM Applications of OC, Thu. 15.5., 14:30 - 15:00 This paper deals with the problem of shipping liquid chemicals using oceangoing vessels. More specifically, it deals with the problem of assigning liquid chemicals and pumps to ship compartments and then determining the optimal pumping schedule of the assigned chemicals into the ship compartments. The problem is handled in a hierarchical manner; the assignment portion of the problem is formulated and solved as a mixed integer program while the pumping schedule is first formulated as a two-point boundary-value optimal control problem, and then solved using newly developed heuristics. Computational experiments show that this treatment of the problem captures the many real world considerations and can be used to model and optimize the operation of large oceangoing vessels. OPTIMAL DEPLOYMENT OF A DUMBELL SATELLITE WITH TENSION CONTROL Alois STEINDL, Institute for Mechanics, Vienna University of Technology Applications of OC, Thu. 15.5., 15:00 - 15:30 We consider the deployment process of a subsatellite from a main satellite on a circular orbit around the earth. Both satellites are connected by a massless tether. By applying a tension force at the cable we want to steer the satellite system from the initial configuration into the stable radial relative equilibrium. In order to avoid destabilization of motion into out-of-plane direction and for safe operation of the deployment mechanism, the length of the tether has to increase monotonically. GLOBAL INDETERMINACY IN TWO-SECTOR MODELS OF ENDOGENOUS GROWTH Paulo BRITO, UECE-ISEG,, Technical University of Lisbon Alain VENDITTI Endogenous Growth, Thu. 15.5., 14:00 - 14:30 In this paper we present a two-sector endogenous growth model where both physical and human capital are produced with externalities that depend upon all aggregate state variables. Therefore, we extend both Uzawa-Lucas and Romer models. In particular, we constrain the technological parameters such that a aggregate production function is homogeneous linear, though the private production function need not to be so, which allow for the existence of a balanced growth path. Global indeterminacy exists when there is multiplicity in the equilibrium long run growth rates while local indeterminacy exists when there is multiplicity in the transition towards a long run balanced growth path. In the relevant literature there are several papers documenting the existence of local indeterminacy. By performing a local bifurcation analysis, we prove that: (1) we may have both global and local indeterminacy; (2) local indeterminacy may be of order two or three, meaning that the stable mannifold may be two- or three-dimensional; (3) indeterminacy arises for several types of utility functions (logarithmic or CRRA) and for several configurations of private and aggregate capital intensities.

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FISCAL POLICY AND MULTIPLE EQUILIBRIA IN A DYNAMIC GENERAL EQUILIBRIUM Jan BRUHA, CERGE - EI, P. O. Box 882 Endogenous Growth, Thu. 15.5., 14:30 - 15:00 This paper presents a dynamic general equilibrium model with productive government spending and increasing returns in production. Depending both on government spending productivity and increasing returns, the model exhibits either a unique steady state or a balanced growth path, which is generally not unique. However, even if the steady state is unique, it might not possess saddle path stability and sunspot equilibria may appear. These dynamic properties of the model depend crucially on parameters of fiscal policy. In recent economic literature, the role of public finance in equilibrium determinacy has been extensively discussed. It was recognized that different fiscal policies have very different impacts on dynamics of the economy and that under some policies, the economies could be easily vulnerable to sunspot fluctuations. However, most papers in this field do not consider the possibility that public spending increase the total factor productivity. Therefore I extend these works by investigating the role of public policy in the presence of positive externalities coming from public spending. The paper characterizes sets of model parameters for which the steady state is saddle, for which there are sunspot equilibria and for which the model exhibits endogenous growth. The obtained results seem to be robust to the numerical values of calibrated parameters. ENDOGENOUS FINANCIAL DEVELOPMENT AND GROWTH Leo KAAS, University of Vienna, Department of Economics Endogenous Growth, Thu. 15.5., 15:00 - 15:30 We analyze a linear growth model with idiosyncratic productivity shocks and self-enforcing intertemporal trades. Agents cannot commit to repay their loans because of insufficient collateral, but the threat of credit market exclusion prevents agents from default. Credit market participation is enforced by endogenously specified credit constraints that are imposed on each agent at each point in time. A dynamic complementarity in these credit constraints gives rise to multiple balanced-growth paths. A high-growth equilibrium with developed credit markets coexists with one or two low-growth equilibria with underdeveloped credit markets. Moreover, low-growth equilibria are more volatile than high-growth equilibria as they are exposed to shocks to the wealth distribution and to sunspot shocks.

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AGREEABLE SOLUTIONS IN COOPERATIVE STOCHASTIC DIFFERENTIAL GAMES David Wing Kay YEUNG, Hong Kong Baptist University, Leon PETROSYAN Stochastic Games, Thu. 15.5., 16:30 - 17:00 Formulation of optimal behaviors for players is a fundamental element in the theory of N-person cooperative games. The players' behaviors (actions and imputations) satisfying some specific optimality principles constitute a solution of the game. In other words, the solution of a cooperative game is generated by a set of optimality principles (for instance, the Nash bargaining solution and the Shapley values). In dynamic games, dynamic stability is required. The dynamic stability of a solution of a cooperative differential game is the property that, when the game proceeds along an "optimal" trajectory, at each instant of time the players are guided by the same optimality principles, and hence do not have any ground for deviation from the previously adopted "optimal" behavior throughout the game. In particular, it ensures that the initially chosen principle of optimality remains optimal throughout the entire game and all players do not have any ground for deviation from the initial plan. In games evolving over time, resolving the problem of dynamic instability may not be easy. The reason is that the optimality principles may fail to apply when the game has reached a certain position, despite the fact that it was satisfies at the outset. Agreeability is a notion under which the extension of the solution policy to the situation with a later starting time and any feasible state dominates the corresponding non-cooperation Nash outcome. In the presence of stochastic elements, agreeability is needed on top dynamic stability. In this paper, we developed an agreeable solution for cooperative stochastic differential games. The imputation distribution procedure of the solution can be identified analytically. An illustration with an explicitly solvable differential game is provided. EQUILIBRIA IN STOCHASTIC DIFFERENTIAL GAMES WITH FRACTAL MODULATION Erhan BAYRAKTAR, Department of Electrical Engineering, Princeton University H. Vincent POOR Stochastic Games, Thu. 15.5., 17:00 - 17:30 Stochastic differential games are considered in a non-Markovian setting. Typically, in stochastic differential games the modulating process of the diffusion equation describing the state flow is taken to be Markovian. Then Nash equilibria or other types of solution such as Pareto equilibria are constructed using Hamilton-Belman-Jacobi (HJB) equations. But in a non-Markovian setting the HJB method is not applicable. To examine the non-Markovian case, this paper considers the situation in which the modulating process is a fractional Brownian motion. Fractional noise calculus is used for such models to explicitly find the Nash equilibria. Although fractional Brownian motion is taken as the modulating process because of its versatility in modeling in the fields of finance and networks, the approach in this paper has the merit of being applicable to any Gaussian stochastic differential games with only slight conceptual modifications. This work has applications in finance to stock price modeling which incorporates the effect of institutional investors, and to stochastic differential portfolio games in markets in which the stock prices follow diffusions modulated with fractional Brownian motion.

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LINEAR QUADRATIC DIFFERENTIAL GAMES: AN OVERVIEW AND ITS USE IN MACRO-ECONOMIC POLICY MODELING. Jacob ENGWERDA, Tilburg University, Stochastic Games, Thu. 15.5., 17:30 - 18:00 In this presentation we give an overview on the theory of indefinite regular linear quadratic differential games. That is, we consider a linear dynamic system which is controlled by different agents. Uncertainty about a correct specification of the object of study is modelled as an additional unknown deterministic component entering the system. We assume that the performance criterion the individual players like to minimize is given by an indefinite linear quadratic function. It is assumed that every player dislikes to use his control instruments. Moreover, we assume that players may have different perceptions about the modelling misspecification. Deviations of the state of the system from zero may both be interpreted in this setting as a desirable phenomenon or as a property which should be avoided. The planning horizon of the players is either finite or infinite. The outcome of this game depends on the information the players have on the game and whether they cooperate or not in pursueing their goals. Both for the open-loop and feedback information structure we discuss the state of the art. In particular the relationship with the solvability of various Riccati equations will be highlighted. Moreover, we flash some numerical aspects. Finally, we illustrate how these concepts and techniques are used in the modelling of a macro-economic policy game. References: 1. Aarle B. van, Engwerda J.C. and Plasmans J., 2002, Monetary and fiscal policy interaction in the EMU: a dynamic game approach, Annals of Operations Research 109, pp.229-264. 2. Basar T. and Olsder G.J., 1999, Dynamic Noncooperative Game Theory, SIAM, Philadelphia. 3. Broek B. van den B., 2001, Uncertainty in Differential Games, Ph.D. Thesis, Tilburg University, The Netherlands. 4. Engwerda J.C., 2003, Linear Quadratic Differential Games, to appear. 5. Feucht M., 1994, Linear-Quadratische Differentialspiele und gekoppelte Riccatische Matrixdifferentialgleichungen, Ph.D. Thesis, Universität Ulm, Germany. 6. Kremer D., 2002, Non-symmetric Riccati Theory and Noncooperative Games, Ph.D. Thesis, RWTH Aachen, Germany. 7. Weeren A.J.T.M., 1995, Coordination in Hierarchical Control, Ph.D. Thesis, Tilburg University, The Netherlands. INCENTIVES FOR RETAILER PROMOTION IN A MARKETING CHANNEL Georges ZACCOUR, GERAD and HEC Montreal, Steffen JORGENSEN, University of Southern Denmark Sihem TABOUBI, HEC MONTREAL Marketing, Thu. 15.5., 16:30 - 17:00 The paper analyzes a differential game model of a two-member marketing channel. A manufacturer invests in national advertising with the purpose of sustaining the image of one of her brands, and her retailer makes local promotions for the brand. The manufacturer has the option of affecting the retailer's efforts by offering to support local promotional efforts. It is well known that uncoordinated decision making in a channel can create "inefficiencies", in the sense that channel members' noncooperative payoffs are less than what they could obtain in a coordinated setup. The paper assumes that the manufacturer takes the role of a channel leader, and that the retailer accepts being a follower. The leader wishes to induce the retailer to implement a certain outcome and, given the leader's announcement, the retailer as a follower can do no better than to react rationally to the leader's strategy. The paper deals with two specific instances of channel coordination: How can the manufacturer, through her choice of marketing strategy, induce the retailer to implement an outcome that (i) is favoured by the channel members as a group, or (ii) is favoured by the manufacturer only? Further, the paper addresses the issue of sustainability since the problem is resolved by designing an incentive such that coordinated outcomes are (Nash) equilibria.

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DYNAMIC COMPETITIVE PRICING AND SPEED OF DIFFUSION Engelbert J. DOCKNER, Department of Business, University of Vienna Gila E. FRUCHTER Marketing, Thu. 15.5., 17:00 - 17:30 The modeling of the adoption of new products in durable goods markets has received a lot of attention in the marketing science literature. The most prominent model within the class of diffusion models is the logistic growth model with innovation and imitation as the driving forces behind new adoptions. In this classical model both the imitation and the innovation coefficients are related to the speed of diffusion, i.e., the amount of time it takes to get from one penetration level to a higher one. Recent empirical marketing research has measured the speed of diffusion for consumer durables and investigated the economic and demographic conditions that cause it to be different for different durables during different periods of time. While the size of the speed of diffusion is an informative quantitative measure, from a firm's strategy point of view it is important to understand how marketing strategy affects diffusion and how the speed of diffusion impacts on a firm's actions. The last issue has received very little attention in the theoretical marketing literature. In this paper we introduce a dynamic model in which we study the link between the speed of diffusion and the pricing policy of a firm over the product life cycle with and without competitive interactions. We find that in case of a monopoly, the speed of diffusion has no impact on a firm's optimal pricing strategy over the product life cycle. If, however, the market is characterized by strategic (oligopolistic) competition, the exogenous speed of diffusion has an important influence on the optimal pricing policy. In particular, we find that higher speeds of diffusion create an incentive to strategically interacting firms to lower their prices. In that sense, the optimal pricing strategy reinforces the adoption process so that on average the total adoption rate increases and diffusion of the product is faster. PROMOTION AND ADVERTISING: COMPLEMENTS OR SUBSTITUTES? Hassan BENCHEKROUN, McGill University, Marketing, Thu. 15.5., 17:30 - 18:00 This paper seeks to determine the impact of retailers'promotion efforts on the image of the product sold. In the advertising literature, advertising a commidity affects the consumption of that commodity via two channels: The advertising effort of the manufacturer of the commodity and the promotion efforts of each of the retailers that sell the commodity to the consumers. The advertising effort of the manufacturer affects positively the sales of all retailers. The advertising effort of the retailer, that we shall refer to as promotion, can have an ambiguous effect on the sales. It positively affects the retailer's demand for the product. It also affects the image of the product,and the goodwill of consumers towards the product. It is this later effect of the promotion effort that we seek to clarify. The advertising literature is devided with respect to the impact of retailers promotion efforts on the stock of goodwill towars the product. The literature can be devided in two groups, a first that group that assumes that promotion contributes to the goodwill towards the commodity, and a second group that assumes that promotions reduces that goodwill. This paper seeks to provide a model where the impact of promotion on goodwill is endogenously determined.

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A STOCHASTIC LINEAR QUADRATIC MODEL FOR AN ADVERTISING CAMPAIGN Alessandra BURATTO, University of Padua, Dipartimento di Matematica Pura ed Applicata Luca GROSSET Marketing, Thu. 15.5., 18:00 - 18:30 We consider a firm that plans the advertising campaign for an event which is characterized by a fixed number of available tickets. The firm controls the event goodwill evolution throughout advertising and it can invest in two advertising channels simultaneously. We assume that the effects of one advertising channel on the event goodwill are deterministic, whereas the other one are stochastic. The goodwill affects the demand which the firm wants to be as close as possible to the congestion threshold when the event takes place. A second objective concerns the cumulated advertising expenditure which the firm wants to be as close as possible to the advertising budget, an exogenous parameter determined by the firm in a preliminary marketing analysis. Finally the firm wants to minimize the total advertising costs. We assume that the advertising cost function is quadratic, as well as the loss functions which represent the objective of approaching the given threshold value. We formulate a linear quadratic stochastic optimal control problem where the advertising expenditure rates in the two channels are the control functions whereas the event goodwill and the cumulated advertising expenditure are the state functions. We first solve the problem without considering the budget constraint. The optimal control problem has a unique state function (goodwill). The optimal policy in a feedback form is found using the Riccati equation technique and we comment on this solution also considering the extreme cases in which the organization can use only one advertising channel, either deterministic, or stochastic. Hence we consider the problem with the budget constraint. As the cost matrix is singular and the state function is bi-dimensional, we find it necessary to use the generalized differential Riccati equation in a matrix version. THE DYNAMICS OF WAGES AND EMPLOYMENT IN A MODEL OF MONOPOLISTIC COMPETITION AND EFFICIENT BARGAINING Ingrid KUBIN, Wirtschaftsuniversität Wien, Pasquale COMMENDATORE, University of Naples Federico II Labour Economics, Thu. 15.5., 16:30 - 17:00 Modern macroeconomic models with a Keynesian flavour usually involve nominal rigidities in wages and commodity prices. A typical microfoundation recurs to wage bargaining in the labour markets and monopolistic competition in the commodity markets (e.g. Blanchard and Giavazzi). A characteristic feature of those models is that deregulating the labour and commodity markets both increase equilibrium employment. However, those models are typically static models which do not specify explicitly the economic process in time. In the following paper, we develop a dynamic macroeconomic model in which commodity markets are characterised by monopolistic competition and labour markets by wage bargaining. In this first version, the number of firms is fixed. The incorporation of firm entry and exit is left for further research. In our analysis the usual equilibrium solution is a fixed point of the dynamic model which exhibits the usual comparative static properties (deregulating the labour and/or the commodity market increases employment). However, depending upon the parameters the fixed point may loose stability through a Flip-bifurcation giving rise to cyclical solutions. We show that commodity and labour market deregulation may lead to instability and may even lower average employment. This result, valid in a dynamic framework, contrasts with the usual comparative static properties.

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THE DYNAMICS OF FRENCH UNEMPLOYMENT: INTERPRETATION AND EMPIRICAL APPLICATION IN TERMS OF STRONG HYSTERESIS Dany LANG, CEDERS - Université de la Méditerranée, Labour Economics, Thu. 15.5., 17:00 - 17:30 The object of the paper is to propose an interpretation in terms of strong hysteresis of the dynamics of the French unemployment over a long period. Hysteresis theories of unemployment have been worked out originally around the end of the 1980’s as an alternative to the theories of “natural unemployment”, to explain the persistence of mass unemployment in Europe. Now, the problem of unemployment is far from being resolved, and yet hysteresis theories have not been much evoked by macroeconomists during the last years. This relative loss of interest for hysteretic models is partly due to the not very conclusive results of the econometrical studies aimed to verify its presence empirically. Actually, in discrete time, the unit root tests, and their equivalent in continuous time, the zero root tests, just as their more recent and elaborate variants, applied to the rate of unemployment, lead, in most of the cases, to the rejection of the hypothesis of hysteresis. Thus, empirical tests would tend to prove the “alternative”, that is, the existence of a self-regulating mechanism bringing back gradually the unemployment rate to a unique and stable “natural” level. In fact, as shown by AMABLE, HENRY, LORDON and TOPOL, the models tested by these papers use a hysteresis definition not true to its original mathematical formulation, which is used in sciences like physics or biology. According to the mathematical definition, due to KRASNOSEL’SKII & POKROVSKII [1989] and MAYERGOYZ [1991], a hysteresis process has a memory of past shocks, this memory being non-linear, selective, and having the property of remanence. The memory is said to be non-linear since the application of a shock of the same extent as an initial shock, but in the opposite direction, does not bring the system back to its initial position. Remanence, in opposition to persistence, means that temporary shocks can have permanent effects. Finally, the property of selectivity makes that only the non-dominated shocks remain in the bank of memory of the system. In economics, if this “strong” hysteresis definition has led to a prolific development in the field of exchange rates, it has, at present, not been often used in the one of employment. One of the reasons of this infatuation lack so far held, partly, to the absence of empirical method allowing to detect the presence of such mechanisms. Now, CROSS & alii [2000] and HALLET & PISCITELLI [2002] recently perfected such a method, allowing in particular to distinguish empirically the hysteretic systems of those possessing near characteristics, as the models of multiple equilibria. Therefore, our paper is aimed to build a labour demand model possessing the strong hysteresis property, then to test it empirically with data concerning the French unemployment. In the model, a large number of heterogeneous firms adjust discontinuously their labour demand in reaction to growth fluctuations. The firms are heterogeneous since each of them owns a couple of “hire-wire” switching point different from the others. The macroeconomic consequence of this behaviour is the presence of hysteresis in the growth-employment relationship. The empirical methodology used to test the presence of hysteresis is a variant of the ones perfected by CROSS & alii [2000] and HALLET & PISCITELLI [2002].

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UNEMPLOYMENT AND INVENTORIES IN THE BUSINESS CYCLE Gerd WEINRICH, Catholic University of Milan, Luca COLOMBO, Catholic University - Milano Labour Economics, Thu. 15.5., 17:30 - 18:00 The paper builds on two previous articles (Bignami, Colombo and Weinrich, “Complex Business Cycles and Recurrent Unemployment in a Non-Walrasian Macroeconomic Model”, forthcoming JEBO, and Colombo and Weinrich, “The Phillips Curve as a Long-Run Phenomenon in a Macroeconomic Model with Complex Dynamics”, forthcoming JEDC) in which dynamic non-tâtonnement macroeconomic models are analyzed. Within each period prices are fixed and an allocation is obtained by means of temporary equilibrium with rationing whereas prices are adjusted between successive periods according to the strength of rationing. A simplifying assumption in the above models is that there are no inventories. The implication is that of the four conceptually possible equilibrium regimes only three actually occur, while states of Underconsumption are never observed. In the present paper this assumption is abandoned. Then there exists, for any given set of parameter values and values of the state variables, a unique temporary equilibrium allocation. In the partition of the price-wage-plane into the different equilibrium regimes the border line between the Underconsumption and Repressed Inflation may have positive or negative slope, depending on the size of stocks. Since stocks are endogenous, this increases further the complexity of the behavior of the dynamic system. Numerical simulations provide new and interesting insights with respect to the dynamic effects of fiscal and monetary policy choices. THE EFFECT OF LONG-SHORT DISTANCE TO CONSUMER CENTERS IN THE OPTIMIZATION OF AQUACULTURE MANAGEMENT Juan HERNÁNDEZ, University of Las Palmas de Gran Canaria, Miguel LEÓN Carmelo LEÓN Renewable Resource Management, Fri. 16.5., 9:00 - 9:30 The aquaculture industry is characterized by its high dependence on environmental conditions. A particular species can reach higher sizes in places with more adequate water temperature or streams. However, these better conditions are usually located far from the consumers centers, as islands. We present in this paper a simple optimal control model applied to seabream culture management. The model includes a growth function for seabream validated with real culture data. We study the most profitable production strategy for farms located in the continental coast (Mediterranean) and in islands (Canary Islands). We obtain a similar rationing recommendations along the culture period for the two regions, clearly below the usually accepted satiation level. However, the optimal commercial size is higher for the island scenario. This conveys the existence of a differential production factor for the long distance culture.

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SUSTAINABLE FOREST POLICIES - AN OPTIMAL CONTROL MODEL Katrin ERDLENBRUCH, INRA-LAMETA, Departement ESR Mabel TIDBALL Renewable Resource Management, Fri. 16.5., 9:30 - 10:00 Pigouvian taxes are one standard tool to internalise externalities linked to natural resources. However, in the forest sector and especially in central Africa, most taxes do not play this role as they do not refer to the ecological state of the forest. Instead, taxes depend on the economic performance of the concessionaire or the concession size. What goes along, havest and export taxes, although they do depend on harvest activity, do not make any difference between sustainable and unsustainable harvesting. This paper proposes two taxes which depend on forest richness and the sustainablility of the concessionaire’s harvesting behaviour. The uderlying model is a deterministic singular optimal control problem with instantaneous unit profits being piecewise differentiable. The first tax is only payable if the forest stock is smaller than the socially desirable stock. The second tax is an extension of the first: it is only payable if the real stock is smaller than the socially desirable and, at the same time, if the harvest rate exceeds the natural growth rate. The steady state of the system varies with both, the initial forest richness and the concessionaire’s behaviour. Both taxes increase the optimal forest stock. Whereas the first allows all concessionaires to reach the same forest stock but is relatively costly to implement, the second tax differentiates between concessionaires and is less costly for most of them. APPLICATIONS OF DYNAMIC PROGRAMMING TO ECONOMIC PROBLEMS WITH VINTAGE Silvia FAGGIAN, Dipartimento di Matematica, Facoltà di Economia, Università di Roma "La Sapienza" Vintage Models 1, Fri. 16.5., 9:00 - 9:30 In this paper we investigate a problem of optimal investment whose main features are the following: - capital goods are of vintage type (i.e. they are a function of time and of their age), - the investment (i.e. the control) is acting also on the boundary (namely, investment in new capital goods is allowed), in the framework introduced by Barucci and Gozzi (Research in Economics, 1998, and Journal of Economics, 2001) and by other authors (see also Feichtinger et al.). We analyse different ways of rephrasing the problem into abstract terms by means of semigroup theory, then we choose a particular setting in order to apply dynamic programming. In particular we show that the value function of the problem satisfies a Hamilton--Jacobi--Bellman (HJB) equation in strong sense, in a suitable Hilbert space, where by ``strong'' we mean pointwise limit of classical solutions of approximating equations. We apply such results to infer the existence of optimal feedback laws and discuss economical implications. AGE-STRUCTURED OPTIMAL CONTROL IN POPULATION ECONOMICS Alexia FÜRNKRANZ, Max Planck Institute for Demographic Research, Gustav FEICHTINGER, Vienna University of Technology Vladimir VELIOV, Vienna University of Technology Vintage Models 1, Fri. 16.5., 9:30 - 10:00 This paper brings both intertemporal and age-dependent features to a theory of population policy at the macro-level. A Lotka-type renewal model of population dynamics is combined with a Solow/Ramsey economy. By using a new maximum principle for distributed parameter control we derive meaningful qualitative results for the optimal migration path and the optimal saving rate. paper available at http://www.demogr.mpg.de/papers/working/wp-2002-045.pdf

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HERD BEHAVIOR AND PRICE FLUCTUATIONS IN FINANCIAL MARKETS Gian Italo BISCHI, University of Urbino, Istituto di Scienze Economiche Laura GARDINI, University of Ancona Mauro GALLEGATI, University of Ancona Roberto LEOMBRUNI, University of Torino Antonio PALESTRINI, University of Ancona Financial Markets, Fri. 16.5., 9:00 - 9:30 In this work we investigate the effects of herding on assets price dynamics during the intra-day trading. We put the focus on the role of interaction among individuals, and we relax both the traditional view of rational expectations of a representative investor and the distinction between chartists and fundamentalists. The aim is to investigate the dynamics emerging in a stock market, when in the investment behavior of its participants we allow for a tendency to mimic the actions of other investors, i.e., to engage in herd behavior. The model, built as a mean-field in a binary setting (buy/sell decisions) is expressed by a three dimensional discrete dynamical system, that can be reduced to a master-slave (or unidirectionally coupled) system, with the driving system formed by the two-dimensional subsystem that governs the dynamics of the excess demand and the difference between the observed price and the reference price, and the driven variable given by the reference price. The analysis of the local stability properties and bifurcations of the driving system in the space of parameters shows different dynamic scenarios, and their consequences on the dynamics of the whole three-dimensional model is discussed. Situations of multistability are observed, characterized by a strong path dependence, i.e. the quantitative and qualitative long-run dynamics of the system are strongly influenced by historical accidents. Studying the local stability of the driving system, we show that when the interaction among individuals is low (i.e. there is negligible herding) the dynamics of price converges monotonically or with oscillations to the reference price prior (the price that agents think will prevail during the day) that is equal to the fundamental value, whereas an increases in the strength of interaction, i.e. if agents give a larger weight to the action of the others, produce a Neimark-Hopf bifurcation and oscillatory dynamics are obtained. For the driven variable (the reference price) these situations give rise to a high sensitivity with respect to small changes of the parameters and/or initial conditions, including the possibility of positive or negative divergence (i.e. sudden uncontrolled increases or crashes of the prices). MULTI-ASSET MARKET DYNAMICS Frank WESTERHOFF, University of Osnabrueck, Department of Economics Financial Markets, Fri. 16.5., 9:30 - 10:00 This paper explores multi-asset market dynamics. We consider a limited number of markets on which two types of agents are active. Fundamentalists specialize in a certain market to gather expertise. Chartists may switch between markets since they use simple extrapolative methods. Specifically, chartists prefer markets which display price trends but which are not too misaligned. The interaction between the traders causes complex dynamics. Even in the absence of random shocks, our artificial markets mimic the behavior of actual asset markets closely. Our model also offers reasons for the high degree of comovements in stock prices observed empirically. JEL classification D84, G12 Keywords heterogeneous agents, technical and fundamental analysis, asset price dynamics, comovements in stock prices

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EXCHANGE RATE DYNAMICS, CENTRAL BANK INTERVENTIONS AND CHAOS CONTROL METHODS Cristian WIELAND, University of Osnabrueck, Department of Ecomics Frank WESTERHOFF, University of Osnabrueck Financial Markets, Fri. 16.5., 10:00 - 10:30 We use a simple chartist-fundamentalist model developed by Day and Huang to explore recent chaos control algorithms as potential candidates for central bank intervention rules. We find that methods such as delayed feedback control, OGY and constant feedback have, in principle, the potential to reduce exchange rate variability and deviations from fundamentals even in the presence of large dynamic noise. CAPITAL RESOURCE SUBSTITUTION, OVERSHOOTING, AND SUSTAINABLE DEVELOPMENT Seiichi KATAYAMA, Rearch Institute for Economics and Business Admini, Kobe University Hassan BENCHEKROUN, McGill University Ngo VAN LONG, McGill University Resource Models, Fri. 16.5., 11:00 - 11:30 In this paper, we study an optimal control problem with two state variables: a man-made capital stock, and a stock of renewable natural resource. Capital and resource are substitutable inputs in the production of the final good. We wish to find the optimal growth path of the economy. We specify parameter values so that there exists a unique steady state with positive consumption. In particular, we ask the following questions: (i) Can it be optimal to get to the steady state in finite time under the assumption that the utility function is strictly concave? (ii) Can finite-time approach paths to the steady state be smooth, in the sense that there are no jumps in the control variables? (iii) Are there non-smooth paths to the steady state? We show that starting from low levels of capital stock and resource stock, the optimal policy consists of three phases. In phase I, the planner builds up the stock of man-made capital above its steady state level, while the resource stock is kept below its steady state level. In phase II, the capital stock declines steadily, while the resource stock continues to grow. In phase III, the economy stays at the steady state. Thus, our model exhibits an interesting "overshooting" property. OF WHALES AND MEN Christos KOULOVATIANOS, University of Cyprus, Resource Models, Fri. 16.5., 11:30 - 12:00 I study a stochastic dynamic oligopoly of renewable resources in which there is a unique symmetric feedback Nash equilibrium. The players’ strategies incorporate the law of renewal of the renewable resource with multiplicative separability from the rest of the game’s structural features. In contrast with previous papers that compare consumer’s welfare in the two extreme cases of monopoly and perfect competition, the model enables a comparison of all market arrangements in which symmetric players have non-trivial market power. I find that it is always the monopoly that yields the highest unconditional mean consumer welfare. In other words, outside a monopolistic setup, the oligopolistic price war leads to increased extraction that reduces the long-run mean of the renewable-resource stock to levels that cannot be compensated by the higher share of supply (in terms of the renewable-resource stock) by multiple firms. Using whaling data for the period 1772-1852 (how many whaling ships were sent to the seas of England the tons of whale oil they brought) I elicit the law of whale reproduction, using cointegration techniques. A Wald test supports that the resulting law of whale reproduction has features that are in accordance with ecological theories. My method supports the proposal that understanding the behavior of fishermen (who understand by rule of thumb how fish reproduce), one can understand the reproduction of a fish species and regulate fishing markets better.

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COMPETITION AND COOPERATION IN NATURAL RESOURCES EXPLOITATION Fabio LAMANTIA, OAAP Department - Faculty of Economics, University of Calabria Gian Italo BISCHI, University of Urbino Lucia SBRAGIA Resource Models, Fri. 16.5., 12:00 - 12:30 Within a game theoretic framework, we analyze a model describing the behavior of a population of agents who strategically interact in the commercial exploitation of a common property renewable resource. This population is assumed to be divided into two groups: cooperators, that decide their harvesting policy by maximizing the overall profit of their group, and defectors, that just maximize their own profit. Firstly we determine the harvested quantities by the two groups in a static game, i.e. the Nash equilibrium which depends on the available resource stock and the population share, then we introduce the dynamic equations that govern the growth of the renewable resource and finally we introduce the replicator dynamics that governs the time evolution of the population share between cooperators and defectors. The role of initial conditions and the effect of regulator’s policies can be investigated by a qualitative study of a two dimensional nonlinear dynamical system that describes the time evolution of the resource stock and the population share between cooperators and defectors. The long run evolution of this dynamical system is analyzed by analytical and numerical methods, and the role of some economic and ecologic parameters is investigated. OPTIMIZATION OF AGE- AND DURATION-STRUCTURED SYSTEMS: APPLICATION TO PREVENTION AND TREATMENT OF HIV Tsvetomir TSACHEV, Bulgarian Academy of Sciences, Institute of Mathematics and Informatics Gustav FEICHTINGER, Vienna University of Technology Vladimir VELIOV, Vienna University of Technology Vintage Models 2, Fri. 16.5., 11:00 - 11:30 Our aim is to analyze a model of the spreading of the Human Immunodeficiency Virus (HIV) typical for some countries in Africa. The tools for influencing the dynamics of the process (the controls) are prevention (promoting nonrisky behaviour) and medical treatment of the infected individuals. We formulate our model as an optimal control problem, the cost being the sum of the direct cost of the prevention and treatment effort and the indirect (social) cost. The model takes into account the age of the individuals, and the duration since becoming infected with HIV. The second time-dimension is particularly important in view of the long incubation period and the variable infectivity of the HIV-epidemics combined with the medical treatment that prolongs the active life of the infected individuals. To do our analysis we embed our problem in a general optimal control framework which extends the classical McKendrick model of population dynamics and involves age and duration dependent state variables. The model consists of first order hyperbolic PDE-s and integral equations that make the dynamics nonlocal. Necessary conditions in the form of a maximum principle are derived. Utilizing the maximum principle we obtain a number of numerical results which allow us to draw some non-straightforward conclusions about the trade-off between prevention and treatment.

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ON THE ROLE OF HETEROGENEITY IN PROBLEMS OF CONTROL OF INFECTIOUS DISEASES Vladimir VELIOV, Institute of Econometrics, OR and Systems Theory, Vienna University of Technology Vintage Models 2, Fri. 16.5., 11:30 - 12:00 We extend a class of models of the evolution of infectious diseases, explicitly taking into account the heterogeneity of the population with respect to the risky behavior of the individual members. The level of risky behavior is represented by a scalar parameter (therefore the model involves a parametrized interconnected family of differential equations) and the heterogeneity is measured by an appropriate weighted deviation from the average. We analyze the dependence of the evolution of the disease (in a short, or in a long time horizon) on the level of heterogeneity of the population and on the initial prevalence. In particular, we prove that in a short run a population with lower heterogeneity is more resistant (than one with higher heterogeneity, ceteris paribus) if the initial prevalence is smaller than 0.5, and less resistant if the initial prevalence is greater than 0.5. Then we introduce a prevention control with an economically meaningful objective function and establish some qualitative results for the optimal control, related to its impact on the level of heterogeneity. A part of the results are established analytically, while others are obtained by numerical experiments. ASSET PRICE AND WEALTH DYNAMICS IN A FINANCIAL MARKET WITH HETEROGENEOUS AGENTS Roberto DIECI, Dip. di Matematica per le Scienze Economiche e Sociali, Università degli Studi di Bologna Carl CHIARELLA, University of Technology, Sydney Laura GARDINI Financial Markets & Money, Fri. 16.5., 11:00 - 11:30 A discrete time model of a financial market is proposed, where the dynamics of prices and wealth arises from the interaction of two groups of agents, fundamentalists and chartists. Each group allocates its wealth between a risky asset and an alternative asset, and the two groups have heterogeneous expectations about asset returns: chartists form their expectations by extrapolating past price changes, while fundamentalists use their superior knowledge of fundamentals. We assume that investors have CRRA utility, so that agents' optimal demands for each asset depend on their wealth. A market maker is assumed to adjust prices at the end of each trading period, on the basis of the excess demand and according to particular stabilizing policies. The model results in a high dimensional nonlinear discrete-time dynamical system, with growing price and wealth processes. Although the model is nonstationary, it is reduced to a stationary system in terms of asset returns and wealth shares of chartists and fundamentalists. The steady states of the system are characterized, and important global dynamic phenomena are studied through numerical investigations. Stochastic simulations are also performed, that show the ability of the model to generate some of the characteristic features of financial time series. MONEY AND EXCHANGE IN AN ECONOMY WITH SPATIALLY DIFFERENTIATED AGENTS Petia MANOLOVA, GREQAM, Charles LAI TONG Christophe DEISSENBERG, GREQAM Financial Markets & Money, Fri. 16.5., 11:30 - 12:00 The impact of money supply on the real variables and on utility is an important question in monetary economics. Most previous works study this impact in representative agent economies, often under perfect foresight. With such a framework, however, the use of fiat money as a medium of exchange cannot be endogenously explained. This paper, by contrast, considers an economy where fiat money is intrinsically necessary for exchange, due to the local structure of interaction among agents. It investigates the transitory and permanent impact of local or global injections of money on the dynamics of exchanged quantities, prices, and individual welfares, and the mechanisms that explain this evolution.

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IMPLEMENTATION OF THE TURING TOURNAMENT Jasmina ARIFOVIC, Simon Fraser University, Department of Economics Richard MCKELVEY Learning 2, Fri. 16.5., 14:00 - 14:30 We propose a two sided tournament, which we call the the Turing Tournament which is designed to encourage development of methods to distinguish between machine and human behavior. Simultaneously, the tournament will encourage development of social scientific models for simulating human behavior in various settings. In this paper, we report on an initial implementation of a two sided Turing Tournament to evaluate learning models in two person repeated games. The objective of the tournament is to find learning algorithms, emulators, that most closely simulate human behavior and find Turing tests, detectors, that most accurately distinguish between humans and machines. We implemented some of the learning models studied in the literature, and found that there are significant differences in data generated by those models and humans. This difference is the greatest in coordination games. We have written the software to implement the Turing Tournament, and are currently running its fully implemented version. TECHNOLOGY ADOPTION WITH PRODUCTION EXTERNALITIES Luca V.A. COLOMBO, Catholic University - Milano, Institue of Economics and Finance Learning 2, Fri. 16.5., 14:30 - 15:00 I investigate the relationship between market power and technology adoption decisions, by studying an economy with imperfect competition, a finite number of consumers and an industrial sector producing a consumption good. The industrial sector is composed of a firm price-taker in the goods market and price-maker in the labor market and a number of self-employed entrepreneurs/workers. Consumers are heterogeneous in that they can supply a fixed amount of labor to the firm, work as self-employed or remain unemployed. When introducing a superior technology, workers’ productivity increases. However, the adoption of a better technology generates a positive externality for workers. By learning the technology, a worker acquires superior skills, which improve her outside options. In turn, this positive externality generates a negative pecuniary externality on the firm (i.e. an increase in labor costs). This double source of non-marketed relations may dampen technological adoption if the firm takes into account the impact of its technology choice on the self-employed decisions. I study this problem by characterizing market equilibrium allocations in a Cournot-Nash and in a von Stackelberg framework. I then focus on the Pareto efficient allocations generated by a social planner internalizing all sources of externalities, and I compare them with market allocations. I finally examine how government intervention can overcome market failure trough policy intervention.

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HOW TO APPROACH ECONOMIC COMPLEXITY: FROM AGENTS TO SYSTEMS Massimo SALZANO, University of Salerno, Learning 2, Fri. 16.5., 15:00 - 15:30 Generally the tools to deal with the complexity scenario are derived from Physics (Mantegna 2000; Stanley et alt.: 2001) or Biology (Eigen: 1992). Taking into account the main characteristics of these discipline we may consider these tools able to deal with question characterised by, (Physics) Variable parameters, Continuous Parameters Physically Defined - Crispy – Cluster, it is "Elements based", Evolving Elements (Class. Mech.), Elements Modifying Controls, Large number of observations, (Biology) Continuous parameters, Fuzzy defined, Fitness, Evolving Agents, Variable Scenarios, Scenery modifying’s controls, (Salzano: 2002 ); (Physics and Biology) Reactive Behaviour. In Physics, some A consider that “the field of phase transitions and critical phenomena scale invariance and universality can be useful in guiding research on a broad class of complex phenomena”, but “while scale invariance has been tested for many years, universality is relatively more rarely discussed”. So, they “develop a heuristic argument that serves to make more plausible the universality hypothesis in both thermal critical phenomena and percolation phenomena, and suggest that this argument could be developed into a possible coherent approach to understanding the ubiquity of scale invariance and universality in a wide range of complex systems.” Biological systems are very often input driven; they do present long time series; and, especially, they are generally characterized by non constancy of the parameters; they are agent driven (Salzano: 2002). Biological systems are what they are because variation occurred by chance and was amplified by natural selection until it originated new species. So much so that Monod claimed life is pure chance . [Chance is a theme in Quantum Theory (Heisenberg's principle) and in Thermodynamics (a state of order is actually realized by scores of random fluctuations) and in Darwin's evolution (amplification of variation by natural selection)]. The economy is perhaps the most complex of all complex systems. Some important authors like Prigogine and others have considered economic as a principal field of application for complexity. But, ... the explicit application of complex approach to economics in these last years has shown some the application the tools derived from other disciplines manifests same limit. In fact, economic systems are very often input driven; they present very short time series; and, especially, they are generally characterized by non constancy of the parameters; they are agent driven and present a "pro-active rational behaviour" (Sacco 1992 ). So, they have a mix of characteristics of both Physical and Biological systems but are pro-active. These features imply the complexity tools derived from physics and biology are only partially useful to explain the economic behaviour. The main difference will be in the way to deal with structural modifications. In fact, the characteristic of evolving heterogeneity of agents in the economic system implies that the reaction of the diverse agents to an exogenous system's change will be different in different time. The interrelation among agents could imply a phenomenon of emergence. This will cause a structural modification that depends on the evolution of the population of agents. So, the tools derived from Physics are not able to explain completely the economic behaviour. While the fact that economic agents could manifest a "pro-active rational behaviour" implies that also the biological derived tools are not able to explain the economic emergence. These features are not only present in economics but also in different amount in many other sectors. As consequence the deepening of complex approach and the study of some tools that could be used for the economic sectors can give rise to a dual effect: a) to increase the understanding of economics; b) to develops new tools useful for a better understanding of complexity. So, we will start with a survey of the main characteristics of physics, biological and economic systems; then, we will propose a simulation based on Pro-Active Heterogeneous Agents-PAHA for developing an Automatic Evolving Economic Control (AECE) in the area of Automatic Stabiliser.

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LEARNING EQUILIBRIA IN A PRODUCTIVE ECONOMY Laurent CELLARIER, University of Southern California, Learning 2, Fri. 16.5., 15:30 - 16:00 Cyclical or chaotic competitive equilibrium trajectories that do not exist under perfect foresight are shown to occur under various learning schemes in a standard two-period overlapping generations economy with productive capital. For a given learning algorithm, these trajectories may exhibit different dynamic properties depending whether the underlying information set accommodates all contemporary data. Under least squares learning, convergence of beliefs does not necessarily imply convergence of the realized dynamics. Thus, relaxing the perfect foresight hypothesis may no longer lead an economy with productive capital to asymptotically converge to a steady state, but may instead generate endogenous fluctuations. CONTROL OF NON LINEAR ECONOMICS SYSTEMS Marisa FAGGINI, University of Naples "Parthenope", Nonlinear Dynamical Systems, Fri. 16.5., 14:00 - 14:30 It is generally accepted that economy belongs to complex systems and both deterministic and stochastic descriptions are needed to define main features of its dynamics. This awareness and consequently the requirement of more realistic models have lead to powerful new concepts and tools to deal with apparently random phenomena that at deeper level could be complex and/or chaotic. Despite the difficult to manage chaotic systems many researchers have been pushed to find a control methods and tools of these systems. The control of nonlinear systems can actually be easier than the control of linear ones, because it might take only a small push to engender a big change in the system. In fact, controlled chaotic systems offer an advantage in flexibility: any one of a number of different orbits can be stabilized by the small control and the choice can be switched from one periodic orbit to an other by very small correction of its parameters, without drastically altering the systems configuration or interfering with their inherent properties. Therefore this richness of possible behaviours in chaotic systems may be exploited to enhance the performance of a dynamical system in a manner that would not be possible to have if the system’s evolution is not chaotic. In this paper after a brief survey about the meaning and methods of chaos control we will indicate a new tools used to detect and control a chaotic behaviour and their application in economics. URBANIZATION AND DEMOGRAPHIC TRANSITION Yuri YEGOROV, Institute for Advanced Studies, Nonlinear Dynamical Systems, Fri. 16.5., 14:30 - 15:00 The present article proposes an alternative mechanism of the second demographic transition. The process of industrialization is driven by land scarcity and technological innovation; it leads to economic growth and goes along with urbanization. We observe significantly lower fertility levels in urban areas in comparison to rural. The microeconomic reason for this effect comes from higher costs of raising children in cities, partly due to higher housing prices. Capital accumulation in industry leads to higher labour productivity and causes rural-urban migration. The dynamic model links microeconomic, macroeconomic and demographic blocks of the model, in a framework of overlapping generations. The continuous version is derived in the limit and contains three nonlinear differential equations for independent dynamic variables: rural population, total population and capital. Such a system has a steady state, but dynamics can be complex. The model suggests that urbanization can work as a stabilizing factor for population growth, and we really observe lower or negative population growth in more urbanized countries. The model predicts that Earth can reach a finite population level, which can be consistent with an equilibrium with nature. However, the transition period can involve a peak of population, causing temporary environmental problems.

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A MOVING HORIZON APPROACH TO DISEQUILIBRIUM DYNAMICS Sander VAN DER HOOG, Universiteit van Amsterdam, Nonlinear Dynamical Systems, Fri. 16.5., 15:00 - 15:30 It is well-known in the literature on price adjustment processes that, in general, a Walrasian tatonnement process need not converge to an equilibrium. The relevant market signals for an adjustment process are based on quantity signals as well as price signals, not merely on excess notional demands as used in a Walrasian tatonnement. This leads to considering different kinds of adjustment processes, i.e. so called non-Walrasian tatonnement processes with mixed price-quantity adjustments. In this kind of process it is not uncommon to use a sequence of fixprice equilibria as the dynamical process. But the question how such equilibria are reached or how the come about as the result of some dynamic disequilibrium process is then put aside. This paper aims at providing a framework in which such questions can be answered. We study a dynamic process with trade outside equilibrium. Non-Walrasian equilibria appear as the fixed points of this process, but a multitude of nonlinear dynamic phenomena can be found. A model is formulated with a moving time-horizon in which the markets open sequentially. Agents not only base their optimal decisions on prices, but also on perceived constraints expected to prevail on the markets. We construct a dynamic process in terms of prices and quantity constraints and study the dynamics of this process. Results are illustrated by computer simulations. A NEW LIGHT ON COURNOT DUOPOLY WITH DIFFERENTIATED PRODUCTS Tamotsu ONOZAKI, Asahikawa University, Department of Economics, Nonlinear Dynamical Systems, Fri. 16.5., 15:30 - 16:00 A Cournot duopoly game with differentiated products is investigated. A new type of demand functions which represents consumer's habitual behavior is introduced. It is shown that multiple attractors coexist and long run states of the system are path-dependent. STOCHASTIC OPTIMAL CONTROL WITH APPLICATIONS TO INVESTMENT PROBLEMS Ulrich RIEDER, Department of Mathematics, University of Ulm Plenary Talk, Fri. 16.5., 16:30 - 17:25 We give a review of classical and recent results on stochastic optimal controls. Emphasis will be given to stochastic Maximum Principles, Hamiltonian Systems and HJB equations. Properties of the value functions and viscosity solutions of the HJB equations are discussed, and the construction of optimal feedback controls is shown. In the second part we present some applications in investment analysis. In particular, we consider the Merton problem in a jump diffusion market and study the case where the investor knows the total number of jumps. For this model of inside information, an optimal policy is derived and computed explicitly in the case of logarithmic and power utility. The optimal portfolio is time-varying and has a jump as soon as a jump occurs for the stock prices.

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OPTIMAL INVESTMENTS WITH VINTAGE CAPITAL. AN APPROACH VIA OPTIMAL CONTROL OF PDE'S Fausto GOZZI, Facoltà di Economia, Università di Roma "La Sapienza" Roberto MONTE Maria Elisabetta TESSITOR Plenary Talk, Fri. 16.5., 17:25 - 18:20 In this seminar we first show how to model the problem of optimal investment with vintage as an optimal control problem for partial differenntial equations. The main features are the following: - capital goods are of vintage type (i.e. they are a function of time and of their age, k(t,s)), and the function k satisfy a partial differential equation of first order which is similar to transport equation and to population dynamics equations. - the control is the investment and act in the interior AND in the boundary of the feasible region (namely, investment in new capital goods is allowed). We show how to apply main optimal control techniques to this problem concentrating mainly on the dynamic programming approach (see e.g. papers of Barucci and Gozzi (Research in Economics, 1998, and Journal of Economics, 2001, Faggian, 2002) and compare it with the approach via the maximum principle (analyzed in papers by Feichtinger et al.). We discuss economic implications of the results.

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List of Participants

ALMEDER Christian University of Vienna School of Business, Economics and Computer Science

[email protected]

ARIFOVIC Jasmina Simon Fraser University Department of Economics [email protected]

ARTINGER Michaela University of Vienna School of Business, Economics and Computer Science

[email protected]

ASADA Toichiro Faculty of Economics Chuo University [email protected]

ASEEV Sergei International Institute for Applied Systems Analysis [email protected]

AZEMOBOR Priscilla Charity School General Administration [email protected]

BAUDISCH Annette Max Planck Institute for Demographic Research Rostock [email protected]

BAYRAKTAR Erhan Department of Electrical Engineering Princeton University [email protected]

BENCHEKROUN Hassan McGill University [email protected]

BISCHI Gian Italo University of Urbino Istituto di Scienze Economiche [email protected]

BRITO Paulo UECE-ISEG, Technical University of Lisbon [email protected]

BRUHA Jan CERGE - EI P. O. Box 882 [email protected]

BURATTO Alessandra University of Padua Dipartimento di Matematica Pura ed Applicata [email protected]

CELLARIER Laurent University of Southern California [email protected]

CERQUETI Roy University of Rome "La Sapienza" DIMADEFA-Facoltà di Economia [email protected]

CHAPPELL David University of Sheffield Department of Economics [email protected]

COLOMBO Luca V.A. Catholic University - Milano Institue of Economics and Finance [email protected]

COMMENDATORE Pasquale University of Naples Federico II Dipartimento di Teoria Economica ed Applicazioni

[email protected]

DAWID Herbert Department of Economics University of Bielefeld [email protected]

DAY Richard H. University of Southern California Department of Economics [email protected]

DEISSENBERG Christophe GREQAM [email protected]

DI LIDDO Andrea Department of Economics, Mathematics and Statistic [email protected]

DIECI Roberto Dip. di Matematica per le Scienze Economiche e Sociali Università degli Studi di Bologna

[email protected]

DOCKNER Engelbert J. Department of Business University of Vienna [email protected]

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DÖRNER Karl University of Vienna School of Business, Economics and Computer Science

[email protected]

EHTAMO Harri Helsinki University of Technology Systems Analysis Laboratory [email protected]

EL OUARDIGHI Fouad ESSEC Business School [email protected]

ELHAFSI Mohsen University of California Graduate School of Management [email protected]

ENGWERDA Jacob Tilburg University [email protected]

ERDLENBRUCH Katrin INRA-LAMETA Departement ESR [email protected]

FAGGIAN Silvia Dipartimento di Matematica, Facoltà di Economia Università di Roma "La Sapienza"

[email protected]

FAGGINI Marisa University of Naples "Parthenope" [email protected]

FEICHTINGER Gustav Vienna Univ. of Technology Department of OR and Systems Theory [email protected]

FLASCHEL Peter Universität Bielefeld Fakultät für Wirtschaftswissenschaften [email protected]

FÜRNKRANZ Alexia Max Planck Institute for Demographic Research [email protected]

GARCÍA Cabo Dept. Economía Aplicada (Matemáticas) Universidad de Valladolid [email protected]

GAUNERSDORFER Andrea University of Vienna School of Business, Economics and Computer Science

[email protected]

GAVRILA Caius Dipartimento di Matematica Universita degli Studi di Roma "Tor Vergata" [email protected]

GOZZI Fausto Facoltà di Economia Università di Roma "La Sapienza" [email protected]

GRASS Dieter Vienna Univ. of Technology Department of OR and Systems Theory [email protected]

GREINER Alfred Bielefeld University [email protected]

HARKS Tobias [email protected]

HARTL Richard F. University of Vienna School of Business, Economics and Computer Science

[email protected]

HAUNSCHMIED Josef L. Vienna Univ. of Technology Department of OR and Systems Theory [email protected]

HERNÁNDEZ Juan University of Las Palmas de Gran Canaria [email protected]

HOFBAUER Josef Institut für Mathematik Universität Wien [email protected]

HOMMES Cars University of Amsterdam CeNDEF [email protected]

JEAN-MARIE Alain LIRMM - University of Montpellier 2 Departement IFA [email protected]

JORGENSEN Steffen University of Southern Denmark Dept. of Organization and Management [email protected]

KAAS Leo University of Vienna Department of Economics [email protected]

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KATAYAMA Seiichi Rearch Institute for Economics and Business Admini Kobe University

[email protected]

KAYODE LUQMAN Adebisi K AY ENGINEEINER NIGERIA LIMITED [email protected]

KIECHLE Günther University of Vienna School of Business, Economics and Computer Science

[email protected]

KITTI Mitri Helsinki University of Technology Systems Analysis Laboratory [email protected]

KNOLL Claudia Vienna Univ. of Technology Department of OR and Systems Theory [email protected]

KOPEL Michael University of Technology Dept of Managerial Econ and IO [email protected]

KORT Peter Department of Econometrics & Operations Research Tilburg University

[email protected]

KOULOVATIANOS Christos University of Cyprus [email protected]

KUBIN Ingrid Wirtschaftsuniversität Wien [email protected]

LAMANTIA Fabio OAAP Department - Faculty of Economics University of Calabria [email protected]

LANG Dany CEDERS - Université de la Méditerranée [email protected]

LEITMANN George College of Engineering, University of california [email protected]

LEUNG Siu Fai Department of Economics Hong Kong University of Science and Technology

[email protected]

LORENZ Hans-Walter Department of Economics University of Jena [email protected]

MANOLOVA Petia GREQAM [email protected]

MARTIN-HERRAN Guiomar GERAD and University of Valladolid [email protected]

MATSUMOTO Akio Chuo University Department of Economics [email protected]

MAURER Helmut Westfälische Wilhelms-Universität Münster Institut für Numerische Mathematik [email protected]

MOSEKILDE Erik Department of Physics The Technical University of Denmark [email protected]

MÜHLBÖCK Elisabeth University of Vienna School of Business, Economics and Computer Science

[email protected]

NECK Reinhard Department of Economics University of Klagenfurt [email protected]

ONOZAKI Tamotsu Asahikawa University, Department of Economics

[email protected]

ORIABURE Augustine Charity School General Administration [email protected]

OYAMA Daisuke University of Vienna Department of Economics [email protected]

PALOKANGAS Tapio Department of Economics University of Helsinki [email protected]

PASCHE Markus Friedrich-Schiller-Universität Jena Lehrstuhl VWL / Makroökonomik [email protected]

PETIT Maria Luisa University of Rome "La Sapienza" [email protected]

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PITTNAUER Verena University of Vienna School of Business, Economics and Computer Science

[email protected]

POLACEK Michael University of Vienna School of Business, Economics and Computer Science

[email protected]

PREUSSER Margaretha University of Vienna School of Business, Economics and Computer Science

[email protected]

PUU Tönu Umeå University CERUM [email protected]

REIMANN Marc University of Vienna School of Business, Economics and Computer Science

[email protected]

RIEDER Ulrich Department of Mathematics University of Ulm [email protected]

RINCÓN-ZAPATERO Juan Pablo

Universidad de Valladolid Dpto. Economía Aplicada (Matemáticas) [email protected]

ROSSER Barkley James Madison University Program in Economics [email protected]

RUBIO Santiago Department of Economic Analysis University of Valencia [email protected]

SALZANO Massimo University of Salerno [email protected]

SEMMLER Willi Universität Bielefeld Lehrstuhl für quantitative Wirtschaftspolitik [email protected]

SORDI Serena Dipartimento di Economia Politica Università di Siena [email protected]

STEINDL Alois Institute for Mechanics Vienna University of Technology [email protected]

SUZUKI Mami Aichi Gakusen University Department of Management [email protected]

TABOUBI Sihem HEC MONTREAL Department of Marketing [email protected]

TAGOE Lawrence Nii Okai nissi business services limited p o box od501 [email protected]

TAPIERO Charles S. ESSEC [email protected]

TIDBALL Mabel INRA-LAMETA Institut National de Recherche Agronomique [email protected]

TODA Maria Vienna Univ. of Technology Department of OR and Systems Theory [email protected]

TORRES Delfim F. M. University of Aveiro Department of Mathematics [email protected]

TRAGLER Gernot Vienna University of Technology Inst. f. Econometrics, OR & Systems Theory [email protected]

TROCH Inge TU Wien [email protected]

TSACHEV Tsvetomir Bulgarian Academy of Sciences Institute of Mathematics and Informatics [email protected]

TUINSTRA Jan Department of Quantitative Economics and CeNDEF University of Amsterdam

[email protected]

VAN DER HOOG Sander Universiteit van Amsterdam [email protected]

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VELIOV Vladimir Institute of Econometrics, OR and Systems Theory Vienna University of Technology

[email protected]

VISCOLANI Bruno University of Padua Department of Mathematics [email protected]

WAGENER Florian CeNDEF Universiteit van Amsterdam [email protected]

WANG Fenfga Fuzhou Huaguang Automatics Technology Co., Ltd. Research & Development

[email protected]

WEINRICH Gerd Catholic University of Milan [email protected]

WESTERHOFF Frank University of Osnabrueck Department of Economics [email protected]

WIELAND Cristian University of Osnabrueck Department of Ecomics [email protected]

WIRL Franz University of Vienna [email protected]

XUE Xigui Fuzhou Huaguang Automatics Technology Co., Ltd. Research & Development

[email protected]

YEGOROV Yuri Institute for Advanced Studies [email protected]

YEUNG David Wing Kay Hong Kong Baptist University [email protected]

ZACCOUR Georges GERAD and HEC Montreal [email protected]

ZUBA Doris Vienna Univ. of Technology Department of OR and Systems Theory [email protected]

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Author-Index

ARIFOVIC.................... 39 ASADA ....................... 16 ASEEV ........................ 20 BAYRAKTAR ............... 28 BEHRENS ................... 12 BENCHEKROUN .....30, 36 BISCHI .............18, 35, 37 BOWON ...................... 24 BRITO......................... 26 BRUHA ....................... 27 BURATTO ................... 31 CAULKINS................... 14 CELLARIER ................. 41 CERQUETI................... 23 CHIARELLA................. 38 COLOMBO .............33, 39 COMMENDATORE ........ 31 DAWID ........................ 10 DAY............................ 10 DEISSENBERG .......10, 38 DIECI .......................... 38 DOCKNER ........20, 24, 30 DODIN ........................ 26 EHTAMO ..................... 19 EL OUARDIGHI ............ 24 ELHAFSI ..................... 26 ELIMAM ...................... 26 ENGWERDA ................ 29 ERDLENBRUCH ........... 34 ESCUDERO ................. 22 FAGGIAN .................... 34 FAGGINI...................... 41 FEICHTINGER..13, 14, 34,

37 FLASCHEL .................. 16 FRUCHTER.................. 30 FÜRNKRANZ ............... 34 GALLEGATI................. 35 GARCÍA ...................... 22 GARDINI ................35, 38 GAVRILA..................... 13

GOZZI..........................43 GREINER .....................20 GROSSET ....................31 GRÜNE ..................10, 17 HARTL...................13, 14 HAUNSCHMIED ............13 HERNÁNDEZ ................33 HOFBAUER ............16, 23 HOMMES .....................23 JEAN-MARIE ................19 JORGENSEN ....22, 24, 29 KAAS ..........................27 KATAYAMA..................36 KITTI ...........................19 KOPEL ........................18 KORT ..............13, 14, 24 KOULOVATIANOS.........36 KRYAZHIMSKII .............20 KUBIN .........................31 LAI TONG ....................38 LAMANTIA ...................37 LANG ..........................32 LAUGESEN ..................21 LEITMANN ...................11 LEOMBRUNI.................35 LEÓN ..........................33 LEUNG ........................25 LORENZ ......................17 MANOLOVA .................38 MARTÍN-HERRÁN .........22 MATSUMOTO ...............19 MAURER......................21 MCKELVEY ..................39 MONTE ........................43 MOSEKILDE .................21 NECK ..........................12 NISHIMURA ..................20 ONOZAKI .....................42 OYAMA........................16 PALESTRINI .................35 PALOKANGAS..............25

PASCHE ...................... 17 PETIT .......................... 25 PETROSYAN ................ 28 POOR.......................... 28 PUU ............................ 17 RIEDER ....................... 42 RINCÓN-ZAPATERO ..... 15 ROSSER ...................... 21 RUBIO ......................... 15 SALZANO .................... 40 SANNA RANDACCIO ..... 25 SBRAGIA..................... 37 SEMMLER........ 10, 16, 17 SORDI ......................... 13 SORGER...................... 23 STEINDL...................... 26 STIEBER...................... 12 SUZUKI ....................... 19 SZIDAROVSZKY ........... 18 TABOUBI ..................... 29 TAKAHASHI ................. 16 TAPIERO ..................... 22 TESSITOR.................... 43 TIDBALL................ 19, 34 TORRES ...................... 11 TRAGLER .............. 13, 14 TSACHEV .................... 37 TUINSTRA ................... 24 VAN DER HOOG ........... 42 VAN LONG................... 36 VELIOV............ 34, 37, 38 VENDITTI ..................... 26 WAGENER ....... 11, 23, 24 WEINRICH ................... 33 WESTERHOFF........ 35, 36 WIELAND..................... 36 WIRL ........................... 15 YEGOROV ................... 41 YEUNG ........................ 28 ZACCOUR.............. 22, 29

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