Evolution of four forms of reciprocity in the prisoner’s dilemma game

Abstract

Reciprocal altruism occurs when individuals help those who help others. It is important as a potential explanation for why human beings have evolved cooperative behavior. Most of the previous studies of reciprocal altruism were based on one of the forms of reciprocity: direct reciprocity, indirect reciprocity, generalized reciprocity, and third-party influence. Recently, several studies have dealt with the interactions among these forms of reciprocity. We constructed a computational model of cooperation in which individuals repeat playing the prisoner’s dilemma game by selecting a strategy based on their behavioral predispositions concerning the four forms reciprocity, and the predispositions evolve according to the game results. We found that a high level of cooperation was achieved only when the population evolved to be dominated by direct reciprocity or dominated by indirect reciprocity. The latter scenarios were further classified into two. The first scenario is direct reciprocity increased, and then indirect reciprocity took the place of it, in addition to the other typical scenario that the indirect reciprocity just grows and dominates the population in the early stage of evolution. It was also suggested that generalized reciprocity could play some role during the course of the evolution of cooperation promoted by direct or indirect reciprocity.