Promotion of cooperation induced by the interplay between structure and game dynamics

We consider the coupled dynamics of the adaption of network structure and the evolution of strategies played by individuals occupying the network vertices. We propose a computational model in which each agent plays a $n$-round Prisoner's Dilemma game with its immediate neighbors, after that, based upon self-interest, partial individuals may punish their defective neighbors by dismissing the social tie to the one who defects the most times, meanwhile seek for a new partner at random from the neighbors of the punished agent. It is found that the promotion of cooperation is attributed to the entangled evolution of individual strategy and network structure. Moreover, we show that the emerging social networks exhibit high heterogeneity and disassortative mixing pattern. For a given average connectivity of the population and the number of rounds, there is a critical value for the fraction of individuals adapting their social interactions, above which cooperators wipe out defectors. Besides, the effects of the average degree, the number of rounds, and the intensity of selection are investigated by extensive numerical simulations. Our results to some extent reflect the underlying mechanism promoting cooperation.