Environment promotes the evolution of cooperation in spatial voluntary prisoner's dilemma game

In reality fitness can be affected by the environment. We explore the evolution of cooperation with the influence of environment on prisoners' dilemma game with voluntary participation. An individual's fitness is redefined to involve one's own payoff and the average performance of neighbors via preference level u. When u equals zero, the game falls back to its traditional form in which the fitness of an individual simply reflects one's own benefit. When u is larger than 0, the environment plays a role. Numerical simulations show that, for small b, increasing u enables the frequency of cooperation to increase monotonously and even dominate the whole population. For large b, although cooperators are exploited by defectors, the existence of loners protects them from getting wiped out. Finally three strategies start to exhibit cyclic dominance.