Active and dormant mechanisms of individual game relationships in evolutionary game theory

In the traditional setup of evolutionary game theory such as the Public Goods Game (PGG), all players are involved in every available group and the game relationships between individuals are undirected and symmetric. Inspired by the exit mechanism in the realistic PGG, i.e., that players would unilaterally choose to quit playing if the payoffs do not meet their expectations, we introduce directionality and asymmetry into the game relationships between players, and propose both active and dormant mechanisms of individual game relationships. In this new scenario, each player would choose to keep unilaterally dormant when his or her payoff is less than the expected value, and become reactivated when certain conditions are satisfied. Our results reveal an optimal region of the expected payoff and the recovery rate, corresponding to the highest frequency of cooperation in the PGG. Spatial distributions of active and dormant groups are obtained to understand the evolution of cooperation.