1 APPLIED MICROECONOMICS Christian Klamler Slides based on: Pindyck R.S. and D.L. Rubinfeld (2009): “Microeconomics”, 7th edition, Pearson International Edition (and on slides by Companion Webpage, Pearson Education). Osborne, M.J. (2004): “An Introduction to Game Theory”, Oxford University Press. Gibbons, R. (1992): “A Primer in Game Theory”, Harvester Wheatsheaf, New York. This work is protected by regional copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the Internet) will destroy the integrity of the work and is not permitted.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
1
APPLIED MICROECONOMICS Christian Klamler
Slides based on: Pindyck R.S. and D.L. Rubinfeld (2009): “Microeconomics”, 7th edition, Pearson International Edition (and on slides by Companion Webpage, Pearson Education). Osborne, M.J. (2004): “An Introduction to Game Theory”, Oxford University Press. Gibbons, R. (1992): “A Primer in Game Theory”, Harvester Wheatsheaf, New York. This work is protected by regional copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the Internet) will destroy the integrity of the work and is not permitted.
n Antoine-Augustine Cournot n John von Neumann; Oskar Morgenstern n John Nash n Nobel-Prize 1994: Harsanyi, Nash, Selten n Nobel-Prize 2005: Aumann, Schelling n Nobel-Prize 2007: Hurwicz, Maskin, Myerson n Nobel-Prize 2012: Roth, Shapley
n relationship between players ¨ cooperative vs. non-cooperative games
n binding contracts
n structure of the game ¨ simultaneous vs. sequential moves
n informational aspects ¨ common knowledge
n information or events that all players know, everybody knows that everybody knows them, everybody knows that everybody knows that everybody knows them, etc.
¨ complete information n each player’s payoff function is common knowledge
¨ perfect information n at each move, the player knows the full history of the game so far
¨ 2 suspects in a major crime are held in separate cells n Enough evidence to convict each of them of a minor offence n Not enough evidence to convict both of them of the major offence unless one
of them acts as an informer (to fink) ¨ They are both independently faced with the following decision problem
n if neither confesses, both get 2 years n if only one confesses he gets 1 year, the other 10 years n if both confess, both get 5 years
20 Solutions n What if there are no dominant strategies?
¨ can we explain behaviour or predict outcome? ¨ best strategy for any given player depends – in general – on the
other players’ actions n rational players n complete information n common knowledge
In case game theory makes a (unique) prediction about the strategy each player should choose, for this prediction to be correct, the players need to be willing to play the predicted strategy.
A Nash equilibrium is an action profile a* with the property that no player i can do better by choosing an action different from ai*, given that every other player j adheres to aj*.
A Nash equilibrium somehow corresponds to a steady state. There is no individual incentive to choose a different strategy. Hence, it embodies a stable “social norm”: if everyone else adheres to it, no individual wishes to deviate from it.
The strategy profile a* is a Nash equilibrium if, for every player i and every action ai of player i, a* is at least as good according to player i’s preferences as the action profile (ai,a-i*) in which player i chooses ai while every other player j chooses aj*. Equivalently, for every player i,
for each strategy ai of player i.
n Notation ¨ a = (a1,…,an) is a strategy profile, i.e. a strategy ai for each player i. ¨ (a’i,a-i) means that all j≠i choose their strategy according to profile
a, while player i chooses strategy a’i ¨ ui(.) is the utility function of player i, which attaches to each
strategy profile the utility that i derives from it.
n We can also define a Nash equilibrium in terms of best response functions:
The strategy profile a* is a Nash equilibrium if and only if every player’s strategy is a best response to the other players’ strategies, i.e. for all players i:
n many situations structurally similar to PD ¨ 2 individuals work on a joint project ¨ each of them can work hard (h) or not (n) ¨ preferences are assumed as follows
¨ based on those preferences, certain payoff functions could lead to the following payoff matrix:
n similar conclusions as in the PD-game n free-rider behaviour n other examples: duopoly, common properties, etc.
30 Nash equilibrium: Matching Pennies n 2 players choose – simultaneously – whether to show the head or
the tail of a coin ¨ If they show the same side, P2 pays P1 one Euro. ¨ If they show different sides, P1 pays P2 one Euro. ¨ What does the payoff matrix look like?
¨ As the players’ interests are diametrically opposed, such a game is strictly competitive and purely conflictual. (zero-sum game)
¨ No Nash equilibrium (at least in pure strategies)
¨ What does the Nash-Cournot equilibrium look like? ¨ What is the collusive outcome?
n but what problems do occur with this outcome?
n What happens if we increase the number of firms? ¨ keep the assumption of identical linear cost functions of the firms ¨ inverse demand function remains P(Q) ¨ what is the Nash equilibrium in this case
¨ the price in the NE of Cournot’s game decreases as the number of firms increases, approaching c
41 Electoral competition n Game theory is important to model the foundation for many
theories of political phenomena n what determines the number of political parties? n what determines the policies that political parties propose? n how is the outcome of an election affected by the electoral system?
n Simple model is a strategic game of the following form: ¨ Players: candidates ¨ Actions: (political) positions (usually numbers on a left-right line) ¨ Preferences: payoff relative to voting outcome
42 Electoral competition n Candidates have certain positions on the line
n Voters have preferences over the positions n the closer the candidate is to a voter’s ideal position, the more the voter
likes this candidate n single-peaked preferences
n In this model, each candidate attracts the votes of all citizens whose favourite positions are closer to her position than to the position of any other candidate.
43 Electoral competition n special position: median
¨ position m with the property that half of the voters’ favourite positions are at most m, and half of them at least m
n Which position should a candidate (in case of 2 candidates only) try to occupy?
median
n Try to be as close to the median as possible to win the election n Hotelling-Downs model of electoral competition n tendency to move towards median position
¨ private value auction n each bidder knows own individual valuation n valuation might differ between bidders n e.g. painting
¨ common value auction n item has same value to all bidders n bidders uncertain about precise value and their estimates differ n e.g. oil fields, party games (glass of coins) n winner’s curse
n Two pricing options: ¨ first-price auction
n sales price equal to the highest bid ¨ second-price auction (Vickrey auction)
n sales price equal to the second highest bid n why should this make sense?
n Nash equilibria in a first-price sealed-bid auction? ¨ is telling the truth a Nash equilibrium?
n (b1, … ,bn) = (v1, v2, v3, … , vn) ¨ what if the bids are (v1-ε,v2,…,vn)? ¨ telling the truth is weakly dominated by other bids ¨ many Nash equilibria
n The second-price sealed-bid auction is the following strategic game ¨ Players: n ≥ 2 bidders ¨ Actions: the set of possible bids bi
¨ Preferences:
n where p is the selling price (i.e. second-highest bid)
n Nash equilibria in a second-price sealed-bid auction? ¨ is telling the truth, i.e. (b1, … , bn) = (v1, … , vn), a Nash equilibrium? ¨ how many Nash equilibria do you find?
¨ could there be a Nash equilibrium in which the player n receives the object?
¨ what happens if we think of the bidding events to unfold over time? n certain equilibria seem to be unreasonable
¨ i.e. for any bid bi ≠ vi, player i’s bid vi is at least as good as bi, no matter what the other players bid, and is better than bi for some actions of the other players.
In a second-price sealed-bid auction a player’s bid equal to her valuation weakly dominates all her other bids.
n A mixed strategy of a player in a strategic game is a probability distribution over the player’s actions.
n a profile of mixed strategies is usually denoted by α n αi(ai) is the probability that player i attaches to her playing action αi
n A strategic game (with vNM preferences) consists of ¨ a set of players ¨ for each player, a set of actions ¨ for each player, preferences regarding lotteries over action
profiles that may be represented by the expected value of a (“Bernoulli”) payoff function over action profiles.
The mixed strategy profile α* in a strategic game with vNM preferences is a (mixed strategy) Nash equilibrium if, for each player i and every mixed strategy αi of player i, the expected payoff to player i of α* is at least as large as the expected payoff to player i of (αi, α-i*) according to a payoff function whose expected value represents player i‘s preferences over lotteries. Equivalently, for each player i
where Ui(α) is a player i‘s expected payoff to profile α.
The mixed strategy profile α* is a mixed strategy Nash equilibrium if and only if αi* is in Bi(α-i*) for every player i.
n mixed strategies NE in addition to NE in pure strategies in a BoS game possible? ¨ P1’s expected payoff in playing “B” is: 2q + 0·(1-q) ¨ P1’s expected payoff in playing “S” is: 0·q + 1·(1-q) ¨ Hence P1 will play “B” as long as 2q > (1-q), what is the case for q >
62 Extensive form games – definitions n Normal form games suppress the sequential structure of decision-
making ¨ we implicitly assumed that each decision-maker chooses her strategy once
and for all n Extensive form games describe the sequential structure of decision-
making explicitly ¨ allow for studying situations in which each decision-maker is free to change
her mind as events unfold ¨ complete and perfect information
n An extensive form game with perfect information has four components: ¨ set of players ¨ a set of sequences (terminal histories) ¨ a player function that assigns a player to every (non-terminal) sequence ¨ for each player, preferences over the set of terminal histories
n An incumbent (I) faces the possibility of entry by a challenger (C) n C as a firm considering entry into an industry occupied by I n C as politician competing for leadership of a party with current leader I n C as an animal competing with another animal (I) for leadership in group
n How does the extensive game work? ¨ At the start of the game and after any (non-terminal) sequence of
events, a player chooses an action ¨ in the entry game, C has the options “in” and “out”
n those actions start the game ¨ I has the option “acquiesce” and “fight”
n what are the strategies for the two players? ¨ player 2 has 4 available strategies: which?
¨ Attention: A strategy of any player i specifies an action for every history after which it is player i’s turn to move, even for histories that, if the strategy is followed, do not occur.
n A strategy profile determines the terminal history that occurs ¨ Let s be the strategy profile and P the player function ¨ Follow the strategies until a terminal history is reached.
n denote this terminal history of s with O(s) n O(s) is a list of actions
1
2C D
E F 2,0
3,1
0,0 1,2
H G 1
Determine O(s) for s = (DG,E)? Determine O(s) for s = (CH,E)?
n As in normal form games, we are interested in equilibria ¨ steady state
The strategy profile s* in an extensive game with perfect information is a Nash equilibrium if, for every player i and every strategy ri of player i, the terminal history O(s*) is at least as good according to player i‘s preferences as the terminal history O(ri,s-i*). Equivalently, for each player i,
for every strategy ri of i.
n How can we find the Nash equilibria in an extensive game? ¨ transform extensive form game into normal form game
The set of Nash equilibria of any extensive game with perfect information is the set of Nash equilibria of it‘s strategic (or normal) form.
A subgame perfect equilibrium is a strategy profile s* with the property that in no subgame can any player i do better by choosing a strategy different from si*, given that every other player j adheres to sj*.
C
Iin out
acq. fight
2,1 0,0
1,2
n Nash equilibrium (out, fight) is not a subgame perfect equilibrium ¨ Strategy „fight“ is not optimal following
the history „in“ n Nash equilibrium (in, acquiesce) is a
82 Properties of subgame perfect equilibrium n First-mover advantage
¨ for any cost and inverse demand functions for which firm 2 has a unique best response to each output of firm 1, firm 1 is at least as well off in any SPE of Stackelberg’s game as it is in any NE of Cournot’s game.
n Can the incumbent make the threat credible? ¨ needs to change the payoffs in the game! ¨ invest in excess capacity, invest in consumer loyalty ¨ this decreases payoffs in case E stays out or enters without fight ¨ increases payoffs in case of fight
C
Iin out
acc fight
5,5-c -1,-1+d
0,10-c
n I will fight if 5-c < -1+d n if this holds, then (out, fight) is a SPNE
85
Markets With Asymmetric Information or The Economics of Information
n what can high-quality seller/agents do? n MARKET SIGNALING
¨ is the process of one agent using signals to convey information to the other agent about the true state
¨ sellers use signals to inform buyers about product’s quality n use guarantees and warranties n cost of warranties to low-quality producers might be too high n importance of reputation and standardization
¨ low-risk individuals try to inform insurers about their risk status ¨ workers try to signal employers their productivity
n weak vs. strong signal
n signals may be inaccurate ¨ design mechanisms to give incentives to let the agents reveal their
93 Moral Hazard n other problems from asymmetric information, besides adverse
selection, ¨ what might happen if you buy a life-insurance? ¨ what might happen if you buy an insurance against theft? ¨ what might happen if you finally got the job?
n MORAL HAZARD ¨ occurs when a party/agent whose actions are unobserved affects
the probability or magnitude of a payment ¨ alters the ability of markets to allocate resources efficiently
n moral hazard not only changes behavior n it also creates economic inefficiency
n Asymmetric information often applies to situations were one person (principal) hires another person (agent) to make economic decisions. ¨ Agency relationship exists whenever there is an arrangement in which
one person’s welfare depends on what another person does. ¨ Principals cannot monitor the productivity of agents perfectly
n PRINCIPAL-AGENT-PROBLEM ¨ agents pursue their own goals, rather than the goals of the principal
n owners hiring managers n patients hiring doctors to decide on treatment n investors hiring financial advisors n car owner/buyer hiring mechanic
n Problem of diverging incentives ¨ Principal needs mechanism to provide incentive for agent to work in
principal’s interest n e.g. reward structure based on long-term performance
97 The Principal-Agent Problem n How can owners design reward systems so that managers and
workers come as close as possible to meeting the owners’ goals? Example: ¨ manager can use low effort (a=0) or high effort (a=1) ¨ firm’s profit also depends on luck, however firm has incomplete
information
bad luck good luck low effort
(a=0) 10,000 20,000
high effort (a=1) 20,000 40,000
¨ manager’s cost function is c=10,000a and she wants to maximize wage ¨ owner’s goal is to maximize expected profit, given uncertainty and
inability to monitor the manager ¨ what is the optimal payment scheme?
98 Asymmetric Information in Labor Markets n Competitive labor market would not allow for unemployment
¨ why do still most countries experience unemployment? ¨ efficiency wage theory
n can explain presence of unemployment and wage discrimination n labor productivity depends on the wage rate
¨ nutritional reasons in developing countries
n In developed countries use shirking model ¨ perfectly competitive market - workers can work or shirk ¨ monitoring workers is costly or impossibility – imperfect information ¨ what if shirkers are detected?
n wage at market clearing rate gives incentive to shirk - firm pays more to make loss from shirking higher
¨ wage at which no shirking occurs is the efficiency wage n but what if all firms pay efficiency wages? n is there again an incentive to shirk?
One of the early examples of the payment of efficiency wages can be found in the history of Ford Motor Company.
Ford needed to maintain a stable workforce, and Henry Ford (and his business partner James Couzens) provided it.
In 1914, when the going wage for a day’s work in industry averaged between $2 and $3, Ford introduced a pay policy of $5 a day. The policy was prompted by improved labor efficiency, not generosity.
Although Henry Ford was attacked for it, his policy succeeded. His workforce did become more stable, and the publicity helped Ford’s sales.
102 Externalities n You are having a party and your neighbor is upset because of the
loud music. What happens here? n You are imposing an EXTERNALITY on your neighbor
¨ the effects of production and consumption activities not directly reflected in the market
¨ Negative externalities n an action by one party imposes a cost on another party n pollution of river by firm upstream affects firms downstream n noise of airplanes affects citizens n negative effect not taken into account by pollutant
¨ Positive externalities n someone’s beautiful garden from which all can benefit (by looking at it)
¨ What if I buy some bread and this raises the price of bread for you? n pecuniary externalities
105 Externalities n Mathematical Model of a production externality
¨ firm 1 produces output q selling it in a competitive market ¨ production of q imposes a cost e(q) on firm 2
equilibrium output q1 is given by P = c’(q1). n firm 1 takes only private costs into account but not social costs n what is the efficient amount of output?
¨ merge the two firms to internalize the externality
leads to a FOC in which price equals marginal social cost
111 Correcting Market Failure n Transferable Emissions Permits
¨ policymaker determines the level of emissions and number of permits ¨ permits are traded in a market ¨ help develop a competitive market for externalities
n firms with high abatement costs will purchase permits from firms with low abatement costs
¨ combines both, standards and fees n allows pollution abatement to be achieved at minimum cost
¨ Examples n Australian carbon trading scheme n Kyoto protocol
115 Stock externalities n so far externalities from flows of harmful pollution n sometimes damage not from emissions flow, but from the
accumulated stock of the pollutant. ¨ e.g. global warming, seen to result from the accumulation of
greenhouse gases (GHG) in the atmosphere n does not cause severe immediate harm n rather the stock of accumulated GHG ultimately causes harm n stock will remain high even if current emission were reduced to zero
¨ also positive stock externalities possible n e.g. the stock of knowledge resulting from investments in R&D
¨ need to compare the present discounted value (PDV) of additional profits resulting from any investment to the cost of the investment
n i.e. need to calculate the net present value (NPV) n cost-benefit analysis n helps to decide whether an investment is economically justified
¨ 100 units of pollutant emitted each year, i.e. Ei = 100 ¨ rate of stock dissipates by 2 percent per year, i.e. δ = 0.02 ¨ stock originally zero, i.e. S0 = 0 ¨ stock creates damage (health costs, etc.) equal to 1 mill. per unit ¨ annual cost of reducing emissions to zero is 15 mill. per unit
118 Stock externalities - Example ¨ Does a policy of zero emission make (economic) sense? ¨ need to calculate the NPV (assuming social rate of discount R)
n costs and benefits of a policy apply to society as a whole n use opportunity cost to society of receiving an economic benefit in the
future rather than today n little agreement on how to use it and its size
¨ NPV depends on discount rate, R, and dissipation rate, δ ¨ numbers for different combinations in the following table:
120 Externalities and Property Rights n active government regulation not only way to deal with externalities n alternative approach: PROPERTY RIGHTS
¨ legal rules stating what people or firms may do with their property ¨ Example: fishermen owning the river
n fisherman can demand compensation from firm upstream polluting the river n hence there is a cost to the firm upstream from polluting the river in form
of this compensation n costs are internalized n via bargaining economic efficiency can be achieved without government
intervention
n COASE THEOREM ¨ if property rights are well specified and parties can bargain without
cost and to their mutual advantage, the resulting outcome will be efficient, regardless of how the property rights are specified
n is bargaining really without cost and are property rights clearly specified?
128 Private preferences for public goods ¨ efficient level of education determined by summing the willingness to
pay of the different individuals (net of tax payments) n leads to an aggregate willingness to pay curve (AW) n hence the efficient outcome is where AW is maximized, i.e. at a spending
of $1200 n is this also the voting outcome? n recall median voter theorem