Promoting cooperation by local contribution under stochastic win-stay-lose-shift mechanism

We introduce a stochastic win-stay-lose-shift (WSLS) mechanism into evolutionary Prisoner’s Dilemma on small-world networks. At each time step, after playing with all its immediate neighbors, each individual gets a score to evaluate its performance in the game. The score is a linear combination of an individual’s total payoff (i.e., individual gain from the group) and local contribution to its neighbors (i.e., individual donation to the group). If one’s actual score is not larger than its desired score aspiration, it switches current strategy to the opposite one with the probability depending on the difference between the two scores. Under this stochastic WSLS regime, we assume that each focal individual gains its fixed score aspiration under the condition of full cooperation in its neighborhood, and find that cooperation is significantly enhanced under some certain parameters of the model by studying the evolution of cooperation. We also explore the influences of different values of learning rate and intensity of deterministic switch on the evolution of cooperation. Simulation results show that cooperation level monotonically increases with the relative weight of the local contribution to the score. For much low intensity of deterministic switch, cooperation is to a large extent independent of learning rate, and full cooperation can be reached when relative weight is not less than 0.5. Otherwise, cooperation level is affected by the value of learning rate. Besides, we find that the cooperation level is not sensitive to the topological parameters. To explain these simulation results, we provide corresponding analytical results based on mean-field approximation, and find out that simulation results are in close agreement with the analytical ones. Our work may be helpful in understanding the cooperative behavior in social systems based on this stochastic WSLS mechanism.