Cooperation in Games with Forgetfulness

Companies and managers are apt to forget information, yet game theory assumes that all players have perfect recall. This paper expands the literature by examining how introducing forgetfulness into a multi-player game-theoretic framework can help or hinder cooperative behavior. We distinguish between forgetting histories and forgetting strategies, and explain how classic game theory models and equilibrium concepts should be adapted to accommodate imperfect recall. We find that forgetfulness impacts the ability of firms to cooperate in countervailing directions. On the one hand, forgetfulness can diminish the ability to punish deviators, making cooperation more difficult. On the other hand, forgetfulness can make meting out severe punishments credible, and if the players forget their strategies then forgetfulness can also decrease the ability for players to effectively deviate, facilitating cooperation. When players forget their strategies, their reduced ability to deviate may be so severe that the equilibrium payoff may be below the minimax