Stochastic adaptation in finite games played by heterogeneous populations
We analyze stochastic adaptation in finite n-player games played by heterogeneous populations containing best repliers, better repliers, and imitators. Individuals select strategies by applying a personal learning rule to a sample from a finite history of past play. We give sufficient conditions for convergence to minimal closed sets under better replies and selection of a Pareto dominant such set. Finally, we demonstrate that the stochastically stable states are sensitive to the sample size by showing convergence to the risk-dominant equilibrium for sufficiently small sample size and to the Pareto-dominant equilibrium for sufficiently large sample size in 2x2 coordination games.
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