Subjective Equilibrium in Repeated Games

Abstract

A player's strategy, for an n-person infinitely repeated game with discounting, is subjectively rational if it is a best response to his individual beliefs regarding opponents' strategies. A vector of such strategies is a subjective equilibrium if the play induced by it is realization equivalent to the play induced by each players' beliefs. Thus, any statistical updating can only reinforce the beliefs. It is shown that under perfect monitoring, the joint behavior at a subjective equilibrium approximates a behavior of a Nash equilibrium even when perturbations are allowed. Therefore, learning processes leading to subjective equilibrium result in approximate Nash behavior.

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