The evolutionary game with asymmetry and variable interaction relations

Abstract

The relations between individuals are usually asymmetric and variable. Considering the different stands and visual angles from different players, we explore the prisoner's dilemma game with two kinds of relations, including the non-negligible and negligible relations. We investigate the proposed model while the initial network structures are the ER random network and the BA scale-free network. Two parameters α and β are set to indicate the individuals' willing to replace their neighbors and the fraction of the initial negligible relations, respectively. The results show that when the initial network structure is the ER random network, the density of cooperators gradually increases with the increase of β, but decreases with the increase of α. Whereas if the initial network topology is the BA scale-free network, the density of cooperators gradually decreases with the increase of β, but increases with the increase of α. Furthermore, regardless of the initial network structure, the stability of the network decreases with the increase of the value of β. In addition, our results show that cooperation could be effectively promoted while the initial network structure is the heterogeneous network.