Scandinavian Working Papers in Economics

SSE/EFI Working Paper Series in Economics and Finance,
Stockholm School of Economics

No 363: Stochastic Imitation in Finite Games

Jens Josephson () and Alexander Matros
Additional contact information
Jens Josephson: Dept. of Economics, Stockholm School of Economics, Postal: P.O. Box 6501, SE-113 83 Stockholm, Sweden
Alexander Matros: Stockholm Institute of Transition Economics and East European Economies, Postal: Stockholm School of Economics, P.O. Box 6501, S-113 83 Stockholm, Sweden

Abstract: In this paper we model an evolutionary process with perpetual random shocks where individual behavior is determined by imitation. Every period an agent is randomly chosen from each of n finite populations to play a game. Each agent observes a sample of population-specific past strategy and payoff realizations. She thereafter imitates by choosing the strategy with highest average payoff in the sample. Occasionally the agents also experiment or make mistakes and choose a strategy at random. For finite n-player games we prove that in the limit, as the probability of experimentation tends to zero, only strategy-tuples in minimal sets closed under the better-reply graph 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. We also show that in 2x2 games the convergence in our model is faster than in other known models.

Keywords: Evolutionary game theory; bounded rationality; imitation; Markov chain; stochastic stability; better replies; Pareto dominance

JEL-codes: C72; C73

33 pages, First version: March 9, 2000. Revised: November 27, 2002. Earlier revisions: November 26, 2002.

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