Cooperation in Networked Prisoner's Dilemma with Individual Learning Feedback

Abstract

Abstract We introduce a modified learning updating mechanism into the evolutionary Prisoner's Dilemma on Newman-Watts (NW) networks. During the evolutionary process, each individual updates its strategy according to individual deterministic switch in combination with a feedback between its score aspiration and actual score. And individual's score is a linear combination of individual's total payoff and local contribution to its neighbors. We study the cooperation level of the system under this learning feedback mechanism, and find that the cooperation level increases as the relative weight of the local contribution to the score increases. In addition, we focus on the influences of learning rate and intensity of deterministic switch in the strategy updating rule on cooperation. Simulations show that for much low intensity of deterministic switch, cooperation is independent of learning rate to a large extent, and full cooperation can be reached when relative weight is not less than 0***.5. Otherwise, cooperation depends on the value of learning rate. Besides, the cooperation level is not sensitive to topological parameters of NW networks. To explain these simulation results, we provide corresponding analytical results of mean-field approximation, and find that simulation results are in good agreement with analytical ones. Our work may shed some light on the maintenance of cooperative behavior in social systems with individual learning feedback.