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Evolutionary Equilibrium with Forward-Looking Players

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Lawrence E. Blume (Cornell University)

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Abstract

The stochastic evolutionary game literature is built on three behavioral postulates: ``noisy'' decisionmaking, myopic decisionmaking and random opportunities for choice (inertia). The role of noise is by now well- understood. This paper investigates the significance of the other two postulates. The model is the conventional evolutionary story, where a population of players is randomly matched against each other, and where strategy revision opportunities for each player arrive at random moments. But here players are assumed to have rational expectations about the evolution of play of their opponents, and choose revision policies to maximize the expected present value of the payoff stream. The dynamic programming problem each player solves is studied, and equilibrium is shown to exist. Not surprisingly, myopic play emerges as discount rates become large. More surprising is that, for any discount rate, myopic play also emerges as the arrival rate of strategy revision opportunities shrinks to~0. These results hold for any $K\times K$ symmetric game. For $2\times 2$ coordination games the effects of taking limits in the opposite direction is studied. When the noise term is small, if players are sufficiently patient or if the arrival rate of strategy revision opportunities is sufficiently large, the unique symmetric Markov equilibrium has each player always choosing the payoff- dominant strategy.

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Paper provided by EconWPA in its series Game Theory and Information with number 9509001.

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Length: 23 pages
Date of creation: 12 Sep 1995
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Handle: RePEc:wpa:wuwpga:9509001

Note: 23 pages plus abstract and cover page, TeX file with one .eps file for a picture on the cover page.
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Find related papers by JEL classification:
C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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  1. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January. [Downloadable!] (restricted)
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  2. Diamond, Peter A, 1982. "Aggregate Demand Management in Search Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 90(5), pages 881-94, October. [Downloadable!] (restricted)
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  3. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July. [Downloadable!] (restricted)
  4. Binmore, Ken, and Larry Samuelson, 1994. "Muddling Through: Noisy Equilibrium Selection," Discussion Paper Serie B 275, University of Bonn, Germany.
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  5. Kiyotaki, Nobuhiro & Wright, Randall, 1989. "On Money as a Medium of Exchange," Journal of Political Economy, University of Chicago Press, vol. 97(4), pages 927-54, August. [Downloadable!] (restricted)
  6. Canning, D., 1990. "Social Equilibrium," Papers 150, Cambridge - Risk, Information & Quantity Signals.
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  1. Lawrence E. Blume, 2003. "Stigma and Social Control," Game Theory and Information 0312002, EconWPA. [Downloadable!]
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