The emergence of rational behavior in the presence of stochastic perturbations
The authors study repeated games where players use an exponential learning scheme in order to adapt to an ever-changing environment. In the presence of stochastic perturbations, this scheme leads to a new stochastic version of the replicator dynamics. The replicator equation obtained is different from the ``aggregate shocks'' approach of evolutionary game theory and it exhibits markedly different rationality properties as well. Irrespective of the perturbations' magnitude, only rationally admissible strategies can survive in the long run. As a result, the game's strict Nash equilibria are stochastically asymptotically stable. The results obtained are illustrated in the case of congestion games.
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