Evolution of cooperation in games with dual attribute strategy

Abstract

Cooperation and defection are two common strategies in game theory. Considering that there may be a kind of middle state between the two as a third option in the real dilemma, we introduce the dual attribute strategy. Compared with cooperation, this strategy possesses the defection attribute, while compared with defection, this strategy possesses the cooperation attribute. Here, it is assumed that players holding the dual attribute strategy play snowdrift games with cooperators based on their defection attribute, meanwhile, they play another snowdrift game with defectors based on their cooperation attribute. Furthermore, we explore the evolution of the three strategies in the well-mixed population and the structured population, respectively. The results show that the dual attribute strategy is more likely to survive. Additionally, the smaller the two kinds of cost-to-benefit ratios are, the more likely cooperation is to exist. Moreover, in the well-mixed population, the existence of cooperation is independent of the temptation to defect. In the structured population, cooperation is more favorable when the cost-to-benefit ratio between the cooperation strategy and the dual attribute strategy is moderate, regardless of the temptation to defect. The dual attribute strategy is actually the embodiment of the simultaneous weakening of cooperation and defection.