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A unified framework of direct and indirect reciprocity

Author

Listed:
  • Laura Schmid

    (IST Austria)

  • Krishnendu Chatterjee

    (IST Austria)

  • Christian Hilbe

    (Max Planck Institute for Evolutionary Biology)

  • Martin A. Nowak

    (Harvard University)

Abstract

Direct and indirect reciprocity are key mechanisms for the evolution of cooperation. Direct reciprocity means that individuals use their own experience to decide whether to cooperate with another person. Indirect reciprocity means that they also consider the experiences of others. Although these two mechanisms are intertwined, they are typically studied in isolation. Here, we introduce a mathematical framework that allows us to explore both kinds of reciprocity simultaneously. We show that the well-known ‘generous tit-for-tat’ strategy of direct reciprocity has a natural analogue in indirect reciprocity, which we call ‘generous scoring’. Using an equilibrium analysis, we characterize under which conditions either of the two strategies can maintain cooperation. With simulations, we additionally explore which kind of reciprocity evolves when members of a population engage in social learning to adapt to their environment. Our results draw unexpected connections between direct and indirect reciprocity while highlighting important differences regarding their evolvability.

Suggested Citation

  • Laura Schmid & Krishnendu Chatterjee & Christian Hilbe & Martin A. Nowak, 2021. "A unified framework of direct and indirect reciprocity," Nature Human Behaviour, Nature, vol. 5(10), pages 1292-1302, October.
    • Handle: RePEc:nat:nathum:v:5:y:2021:i:10:d:10.1038_s41562-021-01114-8
    DOI: 10.1038/s41562-021-01114-8
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    Citations

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    Cited by:

    1. Wu, Yu’e & Zhang, Zhipeng & Yang, Guoli & Liu, Haixin & Zhang, Qingfeng, 2022. "Evolution of cooperation driven by diversity on a double-layer square lattice," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. Quan, Ji & Chen, Xinyue & Wang, Xianjia, 2024. "Repeated prisoner's dilemma games in multi-player structured populations with crosstalk," Applied Mathematics and Computation, Elsevier, vol. 473(C).
    3. Shaohua He & Lei Liu & Qi Liu & Shaoling Fu, 2024. "Creating social value through operational supply chain transparency," Corporate Social Responsibility and Environmental Management, John Wiley & Sons, vol. 31(3), pages 2333-2351, May.
    4. Wang, Xiaoyue & He, Zhixue & Shi, Lei, 2024. "Conformity poses a double-edged sword effect on the evolution of cooperation within heterogeneous endowment populations," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    5. Christian Hilbe & Maria Kleshnina & Kateřina Staňková, 2023. "Evolutionary Games and Applications: Fifty Years of ‘The Logic of Animal Conflict’," Dynamic Games and Applications, Springer, vol. 13(4), pages 1035-1048, December.
    6. Hao, Xinyu & Liu, Guangfu & Zhang, Xiaoling & Dong, Liang, 2022. "The coevolution mechanism of stakeholder strategies in the recycled resources industry innovation ecosystem: the view of evolutionary game theory," Technological Forecasting and Social Change, Elsevier, vol. 179(C).
    7. Zhang, Wei, 2024. "Network reciprocity and inequality: The role of additional mixing links among social groups," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    8. Zhu, Xiaochen, 2023. "The dynamic edge environment under interactive diversity is a double-edged sword," Applied Mathematics and Computation, Elsevier, vol. 436(C).

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