Abstract
Understanding the emergence of cooperation has long been a challenge across disciplines. Even if network reciprocity reflected the importance of population structure in promoting cooperation, it remains an open question how population structures can be optimized, thereby enhancing cooperation. In this paper, we attempt to apply the evolutionary algorithm (EA) to solve this highly complex problem. However, as it is hard to evaluate the fitness (cooperation level) of population structures, simply employing the canonical evolutionary algorithm (EA) may fail in optimization. Thus, we propose a new EA variant named mlEA-CPD-SFN to promote the cooperation level of scale-free networks (SFNs) in the Prisoner’s Dilemma Game (PDG). Meanwhile, to verify the preceding conclusions may not be applied to this problem, we also provide the optimization results of the comparative experiment (EAcluster), which optimizes the clustering coefficient of structures. Even if preceding research concluded that highly clustered scale-free networks enhance cooperation, we find EAcluster does not perform desirably, while mlEA-CPD-SFN performs efficiently in different optimization environments. We hope that mlEA-CPD-SFN may help promote the structure of species in nature and that more general properties that enhance cooperation can be learned from the output structures.
Highlights
The Prisoner’s Dilemma Game (PDG) is a popular abstract mathematical method and has been employed in biology to explain the emergence and persistence of cooperation behavior among selfish individuals[1,2,3,4,5,6,7,8]
The prisoner’s dilemma game (PDG) has long been used to help explain how cooperation endures in nature
The contributions of this paper are summarized as follows: (1) We propose a new evolutionary algorithm (EA) variant named mlEA-CPD-SFN to optimizes the structure of scale-free networks for the promotion of cooperation in the Prisoner’s Dilemma game without changing the initial structures’ degree distribution
Summary
The Prisoner’s Dilemma Game (PDG) is a popular abstract mathematical method and has been employed in biology to explain the emergence and persistence of cooperation behavior among selfish individuals[1,2,3,4,5,6,7,8]. In addition to studying how network reciprocity may influence the evolution of cooperation, some researchers have focused on investigating the potential behavior whereby players may adjust their interaction with others based on the gaming results This is a natural phenomenon since population structure in reality may dynamically change during the game process. While network reciprocity seems to have preliminarily explained large-scale cooperation in reality, some researchers have practically analyzed the real human game Their experiment results revealed that humans do not base their strategy decisions on other’s payoffs while playing PDG. 27 have analyzed cooperation frequency in a simulation where different strategy updating rules are introduced They found cooperation frequency assessed under the imitation-based strategy updating rule depends heavily on the population structure, but network reciprocity seems to have little effect on the game dynamics when individuals do not take neighbors’ payoffs into consideration (non-imitative rule). Carlos et al has emphasized in their research that their conclusion applies only to human cooperation, and network reciprocity may still be relevant to cooperation in other contexts
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