Discrete-time dynamics of indirect reciprocity: The role of punishment

In this paper, we revisit the set-up proposed in Nowak and Sigmund 1998, (NS (1998) henceforth) to study the evolution of social norms when individuals experience forms of indirect reciprocity based on the reputation of agents in the population. A result of the framework in NS (1998) is that cooperative behavior based on the first-order assessment of reputations does not survive in the long run. Cooperators are always victims of a mutation in the population that favors free-riding. We extend the set-up in NS (1998) studying the discrete-time dynamics of the evolution of social norms and introducing an additional form of social sanctioning: individuals who are naturally inclined to act pro-socially may act as enforcers (as in Sethi and Somanathan, 1996) and report free-riders to a third-party authority, which may impose a fine. We show, mainly numerically, that the presence of whistle-blowers, together with the indirect reciprocity of discriminators, allows the existence of equilibria in which cooperation survives, and cooperative agents can co-exist with free-riders in the long run.