Imperfect equilibrium

Imperfect performance equilibrium is defined as a Nash equilibrium where the players' actions may involve noninfinitesimal random errors: each player is endowed with a personal behavior pattern (his performance function) under which the action that he takes depends stochastically on (i) what the player sets out to do, and (ii) the potential consequences that can accrue to him from each of his possible actions. None of the feasible strategies is totally excluded, but the more costly deviations from utility maximization are less likely. An equilibrium identifies both the mutually rational target strategies and the endogenously determined error probabilities. Attractive solutions are shown to emerge in pilot studies of three well-known game models-the coordination game, the repeated prisoner's dilemma, and the chain-store problem. In particular, equilibrium behavior exhibits an appealing sensitivity to how desirable the key outcome is; e.g., cooperation is more likely to arise when the fruits of cooperation are higher. Unlike earlier studies dealing with similar issues, the results for imperfect equilibrium do not depend on asymmetric information or on lengthy repetitions of the game under consideration.