Effects of quasi-defection strategy on cooperation evolution in social dilemma

We introduce the quasi-defection strategy, which acts as a middle state between cooperation and defection. The quasi-defectors need to pay the cost to reward cooperators or punish defectors. The results show that in a well-mixed population, the stable state mainly includes full defection, full quasi defection, three strategies coexist, and the cooperators coexist with the quasi-defectors. Three strategies might coexist through cycle frequency or stable state. The proportion of cooperators tends to increase first and then remains unchanged with increasing punishment. The lost benefits when cooperators are exploited also influence the cooperation evolution. In addition, to some extent, reward can ameliorate the limited impact of punishment and further promote cooperation. The existence of the quasi-defectors can help the cooperators resist the intrusion from the defectors, and the cooperators will tolerate the quasi defectors because of their altruistic behavior, thus facilitating cooperation. Thereby, the quasi-defectors can effectively maintain cooperation in the group.(c) 2022 Elsevier B.V. All rights reserved.