Impact of social reward on the evolution of cooperation in voluntary prisoner?s dilemma

The existence and sustainability of cooperation is a critical issue in nature and social systems. Reward is an essential mechanism to enhance cooperation. Meanwhile, some individuals loathe competition and then choose to escape and become a loner in competition. In this scenario, we propose a four-strategy networked evolutionary game model involving rewarders, loners, cooperators, and defectors. The classical square lattice and the Erdos-Renyi random network are adopted to describe the interaction between individuals. The four -strategy model is an extension of the classic prisoner's dilemma game model. The simulation results show that the introduction of new strategic choices can significantly improve cooperation in the population. The promotion level of cooperation is directly correlated with reward intensity and negatively correlated with reward cost. With regard to the evolution of altruistic behaviors, the fixed income from interactions with loners has an impact that is connected to the temptation to defect. Furthermore, by analyzing characteristic snapshots of four strategies, we further dissect the essence of the evolution of cooperation. As the temptation value increases, cooperators and rewarders first form compact clusters, then more and more loners join to resist the intrusion of defectors. Eventually, the three strategies coexist stably in a spatially structured population. Our research may shed some light on exploring the nature of cooperation and solving social dilemmas in the future.