Impacts of special cooperation strategy with reward and punishment mechanism on cooperation evolution

This paper introduces a special cooperation strategy with both punishment and reward capabilities and analyzes the effect of this strategy on cooperation evolution. The results show that the evolutionary stable states include full defection, the coexistence of ordinary cooperators and defectors, the coexistence of special cooperators and defectors, the coexistence of special cooperators and ordinary cooperators, and the coexistence of the three strat-egies. Punishment can induce cooperation. Under moderate punishment, the greater the reward the more con-ducive to cooperation, while under larger punishment, higher rewards conversely weaken the facilitative effect on cooperation. As the temptation increases, ordinary cooperators decrease to zero, while special cooper-ators increase first and start to decrease or even die out when the ordinary cooperators disappear. The coexis-tence of the three strategies presents that the ordinary cooperator group is exploited by the defectors, the special cooperator group is invaded by the ordinary cooperators, and the defector group is suppressed by the spe-cial cooperators, making the three strategies mutually suppressive and interdependent, and ultimately stable co-existence. The presence of special cooperators significantly promotes cooperation evolution in systems. This contributes to a better understanding of the origins and transformations of social norms and institutions. (c) 2022 Elsevier Ltd. All rights reserved.