Effects of limited interactions between individuals on cooperation in spatial evolutionary prisoner’s dilemma game

We study the spatial evolutionary prisoner’s dilemma game with limited interactions by introducing two kinds of individuals, say type-A and type-B with a fraction of p and (1 − p), respectively, distributed randomly on a square lattice. Each kind of individuals can adopt two pure strategies: either to cooperate or to defect. During the evolution, the individuals can only interact with others belonging to the same kind, but they can learn from either kinds of individuals in the nearest neighborhood. Using Monte Carlo simulations, the average frequency of cooperators ρC is calculated as a function of p in the equilibrium state. It is shown that, compared with the case of p = 0 (only one kind of individuals existing in the system), cooperation can be evidently promoted. In particular, the cooperator density can reach a maximum level at some moderate values of p in a wide range of payoff parameters. The results imply that certain limited interactions between individuals plays an important and nontrivial role in the evolution of cooperation.