Complex Behaviours in binary Choice Models with Global or Local Social Influence Denis Phan (1,2) - Stephane Pajot (1) CREM CNRS Université de Rennes I (2) ICI Université de Bretagne Occidentale AE2006 : A Symposium in Agent-based Computational Methods in Finance, Game Theory and their applications, Aalborg, Denmark, September 14-15. is part of the project 'ELICCIR' supported by the joint program "Complex Systems in Human and Social of the French Ministry of Research and of the CNRS. M.B.G., J-P. N. and D.P. are CNRS members
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Complex Behaviours in binary Choice Models with Global or Local Social Influence
AE2006 : A Symposium in Agent-based Computational Methods in Finance, Game Theory and their applications, Aalborg, Denmark, September 14-15. Complex Behaviours in binary Choice Models with Global or Local Social Influence. Denis Phan (1,2) - Stephane Pajot - PowerPoint PPT Presentation
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Complex Behaviours in binary Choice Models
with Global or Local Social Influence
Denis Phan (1,2) - Stephane Pajot
(1) CREM CNRS Université de Rennes I
(2) ICI Université de Bretagne Occidentale
AE2006 : A Symposium in Agent-based Computational Methods in Finance, Game Theory and their applications, Aalborg, Denmark,
September 14-15.
This work is part of the project 'ELICCIR' supported by the joint program "Complex Systems in Human and Social Sciences“of the French Ministry of Research and of the CNRS. M.B.G., J-P. N. and D.P. are CNRS members
(3) BDD versus GNP model BDD: (Durlauf 1997, Blume, Durlauf 2001, 2003, Brock Durlauf 2001a, 2001b…) GNP: (Nadal et al. 2003, Gordon et al. 2005; Nadal et al. 2005, Phan, Semeshenko 2006)
BBD: Random Utility Model (Thurstone 1927, Luce 1959) + Quantal Choice Analysis (Luce, Supes 1965, McFadden 1974) : idiosyncratic heterogeneity concerns the random term > “Classic Ising Model with annealed disorder”each alternative random term is i.i.d. double exponential (extreme value type I) distributed > probabilistic choices: the join distribution of choice is logistic
GNP: The heterogeneity concerns the fixed idiosyncratic willingness to pay (IWA) > “Quenched Random Field Ising Model” > deterministic maximization
•Plurality of equilibria is a generic propriety of discrete choice models with heterogeneous, idiosyncratic preferences and social influence in case of sufficiently strong social influence, for a large class of mono-modal pdf (Gordon, Nadal, Phan, Semeshenko, 2006)
Part I : Discrete choice with social influence :Agent’s choices and collective outcomeUniqueness vs Multiplicity > hence, coordination plm.
Part II : Multi-Agent Simulation analysis :Finite Size effects; Global or Local interactionsAvalanches et Intermediate equilibrium positions ( due to the irregular discrete distribution of IWA among Agents)
Multiplicity of path-dependant equilibrium positions due to local structures (clusters) Sethna’s hysteresis
Idiosyncratic Willingness to pay distribution: hypothesesGordon, Nadal, Phan, Semeshenko (2006) Discrete Choices under Social Influence: Generic
Properties
H1. Modality: f is unimodal, that is it has a unique maximum.H2. Smoothness: f is non zero, continuous, and at least piecewise twice
continuously differentiable inside its support, ]xm, xM[ , where xm and xM may be finite or equal to ( in the latter case f is strictly monotonically decreasing towards zero as x)
H3 Boundedness: the maximum of f, fB (that may be reached at xm or xM if
these numbers are finite), is finite:prototypical cases
A - Unbounded supports: The support of the distribution is the real axis;
• Typical exemple: the logit distribution (we do not assume that the pdf is symmetric)
•Supplementary hypothesis for extreme values:H 4-5 the pdf has a finite mean value and a finite variance
B- Compact supports: the support of the distribution is some interval[xm, xM] with xm and xM finite; the pdf is continuous on [xm, xM] and continuously derivable on ]xm, xM[ with a unique maximum on [xm, xM].