Effects of dynamic-Win-Stay-Lose-Learn model with voluntary participation in social dilemma

In recent years, Win-Stay-Lose-Learn rule has attracted wide attention as an effective strategy updating rule, and voluntary participation is proposed by introducing a third strategy in Prisoner's dilemma game. Some researches show that combining Win-Stay-Lose-Learn rule with voluntary participation could promote cooperation more significantly under moderate temptation values, however, cooperators’ survival under high aspiration levels and high temptation values is still a challenging problem. In this paper, inspired by Achievement Motivation Theory, a Dynamic-Win-Stay-Lose-Learn rule with voluntary participation is investigated, where a dynamic aspiration process is introduced to describe the co-evolution of individuals’ strategies and aspirations. It is found that cooperation is extremely promoted and defection is almost extinct in our model, even when the initial aspiration levels and temptation values are high. The combination of dynamic aspiration and voluntary participation plays an active role since loners could survive under high initial aspiration levels and they will expand stably because of their fixed payoffs. The robustness of our model is also discussed and some adverse structures are found which should be alerted in the evolutionary process. Our work provides a more rational model and shows that cooperators may prevail defectors in an unfavorable initial environment.