Effects of a membrane formation in the spatial prisoner’s dilemma

Abstract

A cooperative relationship has been developed among individuals. However, altruistic behavior has little advantage against selfish behavior in the sense of rational terms. If each individual chooses selfish behavior pursuing their own payoff, then altruistic behavior will vanish. Earlier studies proposed mechanisms based on game theory which explained the problem of the difference between theoretical predictions and observation. Furthermore, those studies also considered the mechanisms of protecting a cooperator’s cluster in a spatial prisoner’s dilemma involving spatial strategies and spatial generosity, although they did not rigorously analyze the effects of the membrane for the cooperators. In this article, we report the quantitative effect of the membrane for protecting the cooperators from the exploitation of the defectors.