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

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  • Pan, Qiuhui
  • Wang, Yue
  • He, Mingfeng

Abstract

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 strategies. Punishment can induce cooperation. Under moderate punishment, the greater the reward the more conducive 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 cooperators increase first and start to decrease or even die out when the ordinary cooperators disappear. The coexistence 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 special cooperators, making the three strategies mutually suppressive and interdependent, and ultimately stable coexistence. 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.

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  • Pan, Qiuhui & Wang, Yue & He, Mingfeng, 2022. "Impacts of special cooperation strategy with reward and punishment mechanism on cooperation evolution," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    • Handle: RePEc:eee:chsofr:v:162:y:2022:i:c:s0960077922006427
    DOI: 10.1016/j.chaos.2022.112432
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    Cited by:

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    2. Shi, Zhenyu & Wei, Wei & Zheng, Hongwei & Zheng, Zhiming, 2023. "Bidirectional supervision: An effective method to suppress corruption and defection under the third party punishment mechanism of donation games," Applied Mathematics and Computation, Elsevier, vol. 450(C).
    3. Ji, Jiezhou & Pan, Qiuhui & Zhu, Wenqiang & He, Mingfeng, 2023. "The influence of own historical information and environmental historical information on the evolution of cooperation," Applied Mathematics and Computation, Elsevier, vol. 446(C).

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