A comparison of the Moran Process and replicator equations for evolving social dilemma game strategies

Social dilemma games are studied to gain insight into why humans cooperate with other unrelated people. The canonical game has cooperation and defection as the two strategies. Cooperation benefits the group, but a self-interested player can always do better by defecting. But if everybody defects, then the entire group loses. This tradeoff between cooperation and defection gives rise to the social dilemma. Social dilemma games need some method to evolve strategy changes between rounds. The two most widely accepted methods are a Moran process or replicator equations. Although both methods can predict how strategies evolve in a player population, no comparison of their performance has yet been made. In this paper we compare them in a public goods game which is an N-player version of prisoner's dilemma (N>2). Our results indicate only one of these methods should be used in future research efforts.