Stochastic Imitation in Finite Games
SSE/EFI Economics and Finance Working Paper Series No. 363
30 Pages Posted: 8 May 2003
Date Written: November 2002
In this paper we model an evolutionary process with perpetual random shocks, where individuals sample population-specific strategy and payoff realizations and imitate the most successful behavior. For finite n-player games we prove that in the limit, as the perturbations tend to zero, only strategy-tuples in minimal sets closed under single better replies will be played with positive probability. If the strategy-tuples in one such minimal set have strictly higher payoffs than all outside strategy-tuples, then the strategy-tuples in this set will be played with probability one in the limit, provided the minimal set is a product set and the sample is sufficiently large.
Keywords: evolutionary game theory, bounded rationality, imitation, Markov chain, stochastic stability, Pareto dominance
JEL Classification: C72, C73
Suggested Citation: Suggested Citation