The emergence of cooperative behavior based on random payoff and heterogeneity of concerning social image

Abstract

The heterogeneity among individuals in a group usually leads to the volatility of the individual’s income in the game and the difference in the attention paid to the individual’s social image. This paper proposes a spatial prisoner’s dilemma model with random fluctuations of temptation returns and the social images of individuals considered. The payoff of a defector in the game with a cooperator is set as a random variable. And the social image value of an individual who holds the cooperative strategy is set to a positive value, while the social image value of an individual who holds defective strategy is set to zero. Some individuals in the group care about the social images, while others do not. Social image values and benefits are combined into the fitness of individual. The learning strategy adopted is the combination of optimal fitness and Fermi rule based on return difference.Numerical experiments indicate that the volatility of the temptation value is beneficial for cooperation under low temptation, but the volatility of the defector’s income is unfavorable for cooperation under high temptation. And the volatility increases the complexity of system evolution, thereby prolonging the evolution time required to reach steady state. The presence of individuals in the system who care about social image can promote cooperation under low temptation, but the proportion of individuals concerned with social image has little effect on the cooperation behavior. When the social image value of individuals with cooperative strategy increases, the cooperative behavior characteristics of the system do not change qualitatively.