Super-rational aspiration induced strategy updating helps resolve the tragedy of the commons in a cooperation system with exit rights

Avoiding the tragedy of the commons requires altruists to incur some losses to benefit the group. Although specific rules and self-enforcing agreements could help maintain the cooperation system stable, the costly recognition and free-rider problem are still questioned these two cooperation maintenance mechanisms. We here considered the situation of both exit costs and exit benefits in the asymmetric prisoner's dilemma game and introduced a super-rational aspiration induced strategy updating, where players adjust strategies in line with their payoffs and aspirations. If their payoffs reach or exceed the aspiration levels, which may be rational or super-rational, they keep their strategies. Otherwise, they imitate a local neighbor's strategy. We explored this rule in the structured and well-mixed population. The results show that super-rationality and asymmetry could together promote cooperation when exit costs exist. With exit benefit, super-rationality promotes cooperation in both structures and asymmetry only works in the well-mixed population. This suggests that the introduced strategy updating rule could sustain cooperation among egoists with exit rights.