The cooperative evolution in the spatial prisoner's dilemma game with the local loyalty of two-strategy

Abstract

The loyalty of individual strategies is an important factor affecting cooperative behavior in human society. Previous researches on the loyalty have mostly focused on the loyalty of individual to a single strategy, that is, the loyalty of individual to cooperative strategy. But from the perspective of defective strategy, individual holding defective strategy can also be seen as so-called loyalty to defective strategy.This paper presents a spatial prisoner's dilemma game model with the local loyalty of two-strategy, in which the loyalty to cooperative strategy and loyalty to defective strategy are considered simultaneously. To distinguish the loyalties of these two types of strategies, the loyalty value corresponding to defective strategy is represented as a negative number. A fitness of an individual is defined as weighted average of individual's payoff and power of average loyalty of local nearest neighbors. In strategy learning, if the loyalty of an individual and the loyalty of the target neighbor are different signs, a discount coefficient is added to the strategy transition probability function to reduce the probability.Numerical simulations show that considering individual loyalty to the two strategies can promote cooperative behavior in the system when the strength index of local loyalty in fitness function is positive, and there are optimal values for the weighting coefficient and the strength index of local loyalty, which can enable the system to reach full cooperators state. The discount coefficient to the fitness of neighbor can impact on the frequency of cooperators surviving and the proportion of surviving cooperators during phase transition.