Double cyclic dominance promotes cooperation in spatial social dilemmas

The emergence of cooperation is a challenging and important problem. In the realistic world, individuals usually make their opponents cooperate by strengthening the relationship between cooperative neighbors and themselves. Inspired by this phenomenon, a coevolution mechanism is introduced where some individuals can adjust the strength of the relationship between their neighbors and themselves, while others maintain the strength of the relationship regardless of their neighbors' strategies. Through agent-based simulations, we find that cooperative behavior is greatly promoted under the proposed mechanism, and there is an optimal ratio of co-evolutionary individuals for the evolution of cooperation. The potential reason is that under the optimal ratio, the system evolves into three classes which leads to double cycles of individuals with different strategies and weights.