Degree of satisfaction-based adaptive interaction in spatial Prisoner’s dilemma

Abstract

To study why the altruistic cooperation behavior can emerge and maintain among egoistical individuals, researchers across several disciplines have made great contributions for the solutions of this fascinating problem. Ordinarily, the spatial structure is a most often used framework to investigate the cooperative dynamics of evolutionary game. However, very few researchers take into account the reaction of evolutionary game dynamics to interactive intensity between individuals. On account of this, we propose a computational model of automatic adjustment of the interactive intensity based on individual’s degree of satisfaction to study the iterated prisoner’s dilemma game in a two-dimensional square lattice. In this model, selfish individual considers whether the benefits obtained from the other party satisfy its own requirements to determine the intensity of interaction from it to the other party. More specifically, the interactive intensity from an individual x to its some neighbor y is driven by the relations between x obtained current benefit from y (denoted by $$P_{x\rightharpoonup y}$$ ) and x’s satisfaction payoff (denoted by $$S_{p}$$ ). If $$P_{x\rightharpoonup y}>S_{p}$$ , x will increase the intensity of interaction from itself to y; on the contrary, if $$P_{x\rightharpoonup y}<S_{p}$$ , x will weaken the intensity of interaction; other scenarios remain the same. Simulation results show that the proposed mechanism can effectively promote the emergence and maintain of cooperation in population, and the satisfying coefficient $$\alpha $$ ( $$0<\alpha <1$$ ) plays an essential role on cooperation. Interestingly, we found that there are some optimal values $$\alpha $$ that can lead to the best promotion of cooperation. However, individual’s overclaim ( $$\alpha >1$$ ) is not conducive to the effective promotion of cooperation between selfish individuals even for very small temptations to defect. Our results may contribute to the understanding of cooperative dynamics by considering the reaction of evolutionary game dynamics to network.