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To be the fittest is central to proliferation in evolutionary games.Individuals thus adopt the strategies of better performing players in the hopeof successful reproduction. In structured populations the array of those thatare eligible to act as strategy sources is bounded to the immediate neighborsof each individual. But which one of these strategy sources should potentiallybe copied? Previous research dealt with this question either by selecting thefittest or by selecting one player uniformly at random. Here we introduce aparameter $u$ that interpolates between these two extreme options. Setting $u$equal to zero returns the random selection of the opponent, while positive $u$favor the fitter players. In addition, we divide the population into twogroups. Players from group $A$ select their opponents as dictated by theparameter $u$, while players from group $B$ do so randomly irrespective of $u$.We denote the fraction of players contained in groups $A$ and $B$ by $v$ and$1-v$, respectively. The two parameters $u$ and $v$ allow us to analyze indetail how aspirations in the context of the prisoner's dilemma game influencethe evolution of cooperation. We find that for sufficiently positive values of$u$ there exist a robust intermediate $v \approx 0.5$ for which cooperationthrives best. The robustness of this observation is tested against differentlevels of uncertainty in the strategy adoption process $K$ and for differentinteraction networks. We also provide complete phase diagrams depicting thedependence of the impact of $u$ and $v$ for different values of $K$, andcontrast the validity of our conclusions by means of an alternative model whereindividual aspiration levels are subject to evolution as well. Our studyindicates that heterogeneity in aspirations may be key for the sustainabilityof cooperation in structured populations.

Heterogeneous aspirations promote cooperation in the prisoner's dilemma game