**SSE/EFI Working Paper Series in Economics and Finance**
# No 363:

Stochastic Imitation in Finite Games

*Jens Josephson *()

* and Alexander Matros*
**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; (follow links to similar papers)

**JEL-Codes:** C72; C73; (follow links to similar papers)

33 pages, March 9, 2000, Revised November 27, 2002

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