Preferential selection based on payoff satisfaction and memory promotes cooperation in the spatial prisoner's dilemma games

The strategy selection process plays a crucial role in evolutionary dynamics when we study the spontaneous emergence of cooperation under the framework of evolutionary game theory. In most previous studies, it is assumed that individuals choose role models randomly from their neighbors. However, by considering the heterogeneity of individuals' influence in the real society, preferential selection is more realistic. Here, we associate an individuals' attractiveness with payoff satisfaction, which characterized the possibility of changing his strategy. We propose a preferential selection mechanism based on payoff satisfaction and memory in the spatial prisoner's dilemma games on square lattice networks and Erdős-Rényi networks and Barabási-Albert scale-free networks. People might prefer to learn from those with higher satisfaction in real life. Therefore, they are usually more preferable to choose individuals with higher satisfaction when selecting learning role model. We introduce an expected payoff to describe the level of individual satisfaction and memory length to represent the memory capacity of the individual. However, the expectation of defectors and cooperators may be different obviously in the real society. And in general, the expectation of the defector is higher than that of the cooperator. So we want to explore the distribution of expected payoffs that can improve the cooperation level. We investigate the effects of expected payoffs and memory length on cooperation. The results show that cooperation could be promoted when individuals prefer to choose more satisfied neighbors. And the size of expected payoffs and memory length also has different effects on the evolutionary game process. Besides, we investigate the robustness of the network topology, and find that the qualitative features of the results are unchanged