Risk Analysis and Enhancement of Cooperation Yielded by the Individual Reputation in the Spatial Public Goods Game

Abstract

In this paper, an evolutionary game model is put forward to investigate the evolution and risk analysis of cooperation under the spatial public goods game (PGG), in which the individual reputation is obviously utilized to cut down the individual risk of being exploited during the evolution of cooperation. In this model, based on the individual utility, the strategy state will be asynchronously updated according to the Fermi-like rule. Among them, each individual will be initially endowed with an integral reputation value, and then it evolves during the evolution of strategy; while for the individual utility, it is characterized as the product of the game payoff and a power function of reputation value. Monte Carlo simulation (MCS) method is adopted here to verify the system’s evolutionary characteristics, and large quantities of simulations demonstrate that the cooperation behavior can be greatly varied and enhanced when the reputation is incorporated into the utility evaluation. Detailed strategy distribution proves that the individual with large reputation value renders the cooperators to lower their risks to be reaped by defectors, and dominates the evolution of cooperation within the whole population. In addition, the whole cooperation phase diagrams show that the coexistence region of cooperators and defectors becomes narrower and narrower as the reputation is introduced more and more. Meanwhile, it is also displayed that the reputation effect favors the evolution of cooperation, and greatly fosters the cooperators to form the compact clusters so as to reduce the risk of being invaded by defectors. To summarize, current results are conducive to making a deeper insight into the evolution of collective cooperation within many real-world biological and man-made systems.