Evolutionary stability and resistance to cheating in an indirect reciprocity model based on reputation

摘要

Indirect reciprocity is one of the main mechanisms to explain the emergence and sustainment of altruismnin societies. The standard approach to indirect reciprocity is reputation models. These are games in whichnplayers base their decisions on their opponent’s reputation gained in past interactions with other players (moralnassessment). The combination of actions and moral assessment leads to a large diversity of strategies; thusndetermining the stability of any of them against invasions by all the others is a difficult task. We use a variantnof a previously introduced reputation-based model that let us systematically analyze all these invasions andndetermine which ones are successful. Accordingly, we are able to identify the third-order strategies (those which,napart from the action, judge considering both the reputation of the donor and that of the recipient) that arenevolutionarily stable. Our results reveal that if a strategy resists the invasion of any other one sharing its samenmoral assessment, it can resist the invasion of any other strategy. However, if actions are not always witnessed,ncheaters (i.e., individuals with a probability of defecting regardless of the opponent’s reputation) have a chance tondefeat the stable strategies for some choices of the probabilities of cheating and of being witnessed. Remarkably,nby analyzing this issue with adaptive dynamics we find that whether an honest population resists the invasion ofncheaters is determined by a Hamilton-like rule, with the probability that the cheat is discovered playing the rolenof the relatedness parameter.