Evolutionary prisoners dilemma game with voluntary participation on regular lattices and scale-free networks

The voluntary participation mechanism has been demonstrated as a natural extension to promote the cooperative behavior in evolutionary games. Apart from the cooperator strategy and defector strategy in the original Prisoner’s Dilemma Game (PDG), players can choose the additional loner strategy to refuse to participate and get some small but fixed income Q. We allow for voluntary participation in the evolutionary PDG on regular lattices and scale-free networks, and focus on the strategy density and the evolution behavior of the system. Simulation shows that the system behavior is sensitive to the population structure. For lattices, the densities of cooperator, defector and loners exhibit non-trivial behaviors with the increment of Q and temptation parameter b except for the density of loners as a function of Q. For scale-free networks, the densities of cooperator and defectors monotonously decrease with the increment of Q, and the densities of defectors and loners monotonously increase with the increment of b. Moreover, this extension can lead to “rock-scissors-paper”-like cyclic dominance of the three types of players on regular lattices. But for scale-free networks, the loners cannot coexist with cooperators or defectors.