On the evolution of altruistic behavior in asynchronous environments

The prisoner's dilemma is widely accepted as a standard model for studying the emergence of mutual cooperation, within populations of selfish individuals. Simulation studies of the prisoner's dilemma, where players make probabilistic choices based on previous actions, find that strategies such as win-stay-lose-shift, tit-for-tat, and firm-but-fair come to dominate the long term-behavior of the population. Often these models assume that decisions are made in synchrony. In many biological contexts this is an unrealistic assumption, as individuals change their behavior on different and uncorrelated time scales. Here we develop a model where both, one or neither players can update their behavior. We demonstrate that as the assumption of synchrony is relaxed, less reactive and more generous strategies such as firm-but-fair come to dominate the long term population dynamics.