Coevolution of Third-Party Punishment and Punishment Reputation Dependency

Abstract

An obstacle in explaining the evolution of cooperation through third-party punishment is the second-order free rider problem, that is, if punishing others is costly, it is adaptive for any individual not to punish. One hypothesis to resolve the issue states that third-party punishment is advantageous for the punisher, because it is evaluated as socially good and thereby enhances future cooperation from the observers. However, it is thus far unclear whether cooperation is truly promoted by third-party punishment in the presence of a social norm favoring punishing behavior, and under what circumstances such social norm is established. In this paper, we present two mathematical models to explore the reputation-enhancing effect of third-party punishment and its role in the evolution of cooperation. Our results suggest that third-party punishment can indeed facilitate the evolution of cooperation when individuals base their evaluation of others on their punishing behavior, and such punishment reputation dependency can coevolve with third-party punishment during the process where large-scale cooperation is established within a population.