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Stochastic imitation in finite games

  • Josephson, Jens
  • Matros, Alexander

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.

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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 49 (2004)
Issue (Month): 2 (November)
Pages: 244-259

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Handle: RePEc:eee:gamebe:v:49:y:2004:i:2:p:244-259
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