Evolution of prosocial punishment in unstructured and structured populations and in the presence of antisocial punishment
A large body of empirical evidence suggests that humans are willing to engage in costly punishment of defectors in public goods games. Based on such pieces of evidence, it is suggested that punishment serves an important role in promoting cooperation in humans, and possibly other species. Nevertheless, theoretical work has been unable to show how this is possible. The problem originates from the fact that punishment, being costly, is an altruistic act and its evolution is subject to the same problem that it tries to address. To suppress this so-called second-order free-rider problem, known theoretical models on the evolution of punishment resort to one of the few established mechanisms for the evolution of cooperation. This leaves the question that whether altruistic punishment can evolve and give rise to the evolution of cooperation, unaddressed. Here, by considering a population of individuals who play a public goods game, followed by a public punishing game, introduced here, we show that altruistic punishment indeed evolves and promotes cooperation, in a general environment and in the absence of a cooperation favoring mechanism. Besides, our analysis shows, being close to a physical phase transition facilitates the evolution of altruistic punishment.