Evolution of Cooperation in Continuous Prisoner's Dilemma Games on Barabasi—Albert Networks with Degree-Dependent Guilt Mechanism

Abstract

This paper studies the continuous prisoner's dilemma games (CPDG) on Barabasi—Albert (BA) networks. In the model, each agent on a vertex of the networks makes an investment and interacts with all of his neighboring agents. Making an investment is costly, but which benefits its neighboring agents, where benefit and cost depend on the level of investment made. The payoff of each agent is given by the sum of payoffs it receives in its interactions with all its neighbors. Not only payoff, individual's guilty emotion in the games has also been considered. The negative guilty emotion produced in comparing with its neighbors can reduce the utility of individuals directly. We assume that the reduction amount depends on the individual's degree and a baseline level parameter. The group's cooperative level is characterized by the average investment of the population. Each player makes his investment in the next step based on a convex combination of the investment of his best neighbors in the last step, his best history strategies in the latest steps which number is controlled by a memory length parameter, and a uniformly distributed random number. Simulation results show that this degree-dependent guilt mechanism can promote the evolution of cooperation dramatically comparing with degree-independent guilt or no guilt cases. Imitation, memory, uncertainty coefficients and network structure also play determinant roles in the cooperation level of the population. All our results may shed some new light on studying the evolution of cooperation based on network reciprocity mechanisms.