Heterogeneous aspirations promote cooperation in the prisoner's dilemma game

To be the fittest is central to proliferation in evolutionary games. Individualsthus adopt the strategies of better performing players in the hope of successfulreproduction. In structured populations the array of those that are eligible toact as strategy sources is bounded to the immediate neighbors of eachindividual. But which one of these strategy sources should potentially becopied? Previous research dealt with this question either by selecting thefittest or by selecting one player uniformly at random. Here we introduce aparameter that interpolates between these two extreme options.Setting equal to zero returns the random selection of theopponent, while positive favor the fitterplayers. In addition, we divide the population into two groups. Players fromgroup select their opponents as dictated by the parameter, while players from group do so randomly irrespective of. We denote the fraction of players contained in groups and by and , respectively. Thetwo parameters and allow us to analyze in detail how aspirations in thecontext of the prisoner''s dilemma game influence the evolution ofcooperation. We find that for sufficiently positive values of there exist a robust intermediate for which cooperation thrives best. The robustness ofthis observation is tested against different levels of uncertainty in thestrategy adoption process and for differentinteraction networks. We also provide complete phase diagrams depicting thedependence of the impact of and for different values of , and contrast thevalidity of our conclusions by means of an alternative model where individualaspiration levels are subject to evolution as well. Our study indicates thatheterogeneity in aspirations may be key for the sustainability of cooperation instructured populations.