Network adaption based on environment feedback promotes cooperation in co-evolutionary games

Abstract

In evolutionary games, the choices of individuals form the cooperation environments, and the environments in turn affect the behaviors of individuals. Such environment feedback can be utilized to facilitate the evolution of cooperation. On the other hand, adaptive social structures have been thought to promote cooperation, in which the individuals can switch their interacting neighbors. Here, we propose a co-evolutionary game model, in which individuals can adjust connections based on environment feedback during the evolution. In particular, the individuals determine whether to adjust their connections by comparing the local cooperation environment with the global one. Meanwhile, we use the parameter ω to adjust the time scale between the strategy evolution and the network adaptation in the co-evolutionary dynamics. Our results show that, the network adaption based on the environment feedback can significantly promote cooperation. We find that, relatively fast network adaptation (large ω) can better facilitate the evolution of cooperation. We further investigate how the rationality of individuals in network adaptation process affects the cooperation, and find that a high level of rationality is beneficial to improve cooperation. Through monitoring the local cooperation environments of the individuals, the fractions of the reconnecting individuals and the average degrees of cooperators and defectors, respectively, we provide some intuitive explanations for the promotion of cooperation by the co-evolutionary scheme. Our results may provide some references on the study about how to improve cooperation by adapting the social structures based on environment feedback in the real world.