Evolutionary dynamics in voluntary prisoner's dilemma game with environmental feedbacks

It is well known that individual behavior will be influenced by the environment, and likewise, the environment will also change as the individual behavior changes. Based on the voluntary prisoner's dilemma game proposed by Szabó et al., we propose a form of environmental feedbacks reflected in individual fitness in spatial structured population. Through theoretical analysis and numerical simulation, it is found that the level of the cooperation can be improved when the environmental feedback is taken into account. There exists a critical value for the parameter of the temptation to defect (b) that the frequency of cooperators undergoes a sudden rapid increase when b increase and the cooperators could completely dominate the whole population.