Evolutionary public goods games based on historical payoffs

Abstract

We investigate the evolution of cooperation in public goods game based on individuals’ historical payoffs. In particular, the fitness of individuals are characterized by two types of payoffs, which are obtained by acting as cooperators and defectors, respectively. Both of payoffs are the linear combination of the current payoffs and the cumulative historical payoffs. The results show that cooperation is enhanced by an increasing memory effect with a wide range of related factors. To explain this phenomenon, we plot some representative snapshots of the population and scrutinize the mean fitness of cooperators and defectors along the boundary. It is found that increasing memory effect induces a positive feedback mechanism for cooperators to expand their districts. Defectors can just survive through forming narrower clusters to exploit cooperators more widely. The threshold values for cooperators and defectors vanishing under the influence of noise are also investigated.