Aspiration-dependent strategy persistence promotes cooperation in spatial prisoner's dilemma game

Abstract

In this paper, we introduce an aspiration-dependent persistence into the spatial prisoner's dilemma game aimed at promoting cooperation in a population. Based on aspiration, a player could adjust his/her strategy persistence level during the evolutionary process. In particular, he/she will hold a strategy longer if it brings him/her a satisfactory payoff, otherwise he/she will decrease the time duration of keeping the present choice. We also introduce a tunable parameter to characterize the sensitivity of strategy persistence to aspiration and investigate the effects of the sensitivity on the evolution of cooperation. The results show that aspiration-dependent strategy persistence could effectively promote cooperation. At an intermediate aspiration, diverse strategy persistence levels among population could be formed during the evolution, which ultimately results in the highest cooperation level. Then, we present intuitive explanations for the existence of optimal aspiration by scrutinizing the microscopic evolution of cooperation. Moreover, we find that, in the population where individuals are more sensitive to aspiration, cooperation could be further promoted by assembling greater cooperator clusters with the help of diverse strategy persistence distribution. Our results highlight the more realistic scenario where aspiration-dependent persistence is involved in the spatial prisoner's dilemma game.