Does imperfect information always disturb the evolution of reciprocity?

Abstract

Reciprocity has long been regarded as a potential explanatory mechanism for the maintenance of cooperation. However, a possible problematic case relevant to the theory of reciprocity evolution arises when the information about an opponent’s behavior is imperfect. Although it has been confirmed that imperfect information disturbs the evolution of reciprocity, this argument is based on the assumption that those who attempt to cooperate always succeed in doing so. In reality, mistakes can occur, and previous studies have demonstrated that this can sway the evolution of reciprocity. In this study, removing the assumption that mistakes do not occur, we examine whether imperfect information disturbs the evolution of reciprocity in the iterated prisoner’s dilemma game with errors in behavior. It might be expected that when mistakes occur, reciprocity can evolve more in the case of imperfect information than in the case of perfect information. This is because in the former case, reciprocators can miss defections incurred by other reciprocators’ mistakes owing to imperfect information, which allows cooperation to persist. Contrary to this expectation, however, our analysis reveals that imperfect information still disturbs the evolution of reciprocity when mistakes occur. Additionally, we have determined that the condition under which reciprocity evolves remains unaffected, whatever reciprocators subsequently do when the opponent's last behavior was missed.