Evolutionary prisoner’s dilemma game on signed networks based on structural balance theory

Abstract

Evolutionary game has applications in many fields, from engineering to economics and social sciences. Applying evolutionary games to complex networks has become a hot research field. In real society, due to different personalities or interests, friendship or hostility will be established between people, and the alienation or closeness of the relationship will have a greater impact on the game. However, the existing evolutionary game studies on networks rarely comprehensively involve the multiplicity of this relationship. Trying to fill this gap, in this paper, we propose a new Signed-PD (prisoners’ dilemma) game model and derive the fixation probability formula. In our model, we introduce a trust factor and a modified Fermi function to characterize the impact of different relationships on the payoff matrix and strategy imitation respectively. Moreover, the theory of structural balance is extended by taking into account the nodes’ strategy, and a new structural balance rate calculated from energy functions is introduced to reflect structural balance changes. We explore the effect of trust factors on network game and study the impact of game parameters as well as network parameters on evolution, and investigate the impact of monotonic structural balance increasing on the evolution of cooperation in signed networks. Simulation results show that if the temptation value is below a certain threshold, the Game structural balance will change its qualitative dynamics. Furthermore, when the classical structural balance has a monotonic growth control beginning at 0, it can successfully boost the cooperator’s survival.