Altruistic Punishment: the Bridge Leading to the Other Side of the Evolution

In this paper, in order to study the strategic interactions between “cooperation”, “defection” and “altruistic punishment”, a mutation-selection dynamic, with the Prisoner's Dilemma as the background, has been established on an embedded Markov chain, proved the following conclusions: First, the “altruistic punishment”, even though not a Nash equilibrium, can be the only mutation-selection equilibrium when the population size goes to infinity; Second, the “cooperation”, even if been strictly dominated by the defection and altruistic punishment in the matrix game, will be the unique equilibrium of the evolutionary dynamics as the population size approaches infinity; that is to say, the altruistic punishment, even in very weak conditions, can effectively promote the evolution of cooperation.