The effects of nonlinear imitation probability on the evolution of cooperation

In this paper, we introduce a nonlinear imitation rule into an evolutionary prisoner’s dilemma game and investigate how the nonlinear imitation rule affects cooperation. Based on the original version of the proportional imitation rule, the imitation probability for each individual is regulated by a parameter αα, which tunes the dependence of the imitation probability on the payoff difference. The results show that there exists an optimal value of αα at which the cooperation level reaches its highest value. We carry out the simulations in different types of networks with different mean degrees. Results show that the optimal behavior of cooperation induced by the variation of αα is robust. More importantly, from the results we can conclude that there are two crucial factors determining the optimal behavior of cooperation: One is the parameter αα, and the other is the regime of payoff difference supporting strong variation of the dependence of the imitation probability on the payoff difference.