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Title:Stochastic adaption in finite games played by heterogeneous populations PDF Logo
Authors:Josephson, Jens
Issue Date:2001
Series/Report no.:SSE/EFI Working Paper Series in Economics and Finance 475
Abstract:In this paper, I analyze stochastic adaptation in finite n-player games played by heterogeneous populations of myopic best repliers, better repliers and imitators. In each period, one individual from each of n populations, one for each player role, is drawn to play and chooses a pure strategy according to her personal learning rule after observing a sample from a finite history. With a small probability individuals also make a mistake and play a pure strategy at random. I prove that, for a sufficiently low ratio between the sample and history size, only pure-strategy profiles in certain minimal closed sets under better replies will be played with positive probability in the limit, as the probability of mistakes tends to zero. If, in addition, the strategy profiles in one such set have strictly higher payoffs than all other strategy profiles and the sample size is sufficiently large, then the strategies in this set will be played with probability one in the limit. Applied to 2x2 Coordination Games, the Pareto dominant equilibrium is selected for a sufficiently large sample size, but in all symmetric and many asymmetric games, the risk dominant equilibrium is selected for a sufficiently small sample size.
Subjects:Bounded rationality
Evolutionary game theory
Imitation
Better replies
Markov chain
Stochastic stability
Pareto dominance
Risk dominance
JEL:C72
C73
Document Type:Working Paper
Appears in Collections:SSE/EFI Working Paper Series in Economics and Finance, EFI - The Economic Research Institute, Stockholm School of Economics

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