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Partners and rivals in direct reciprocity

Author

Listed:
  • Christian Hilbe

    (Harvard University
    IST Austria)

  • Krishnendu Chatterjee

    (IST Austria)

  • Martin A. Nowak

    (Harvard University
    Harvard University)

Abstract

Reciprocity is a major factor in human social life and accounts for a large part of cooperation in our communities. Direct reciprocity arises when repeated interactions occur between the same individuals. The framework of iterated games formalizes this phenomenon. Despite being introduced more than five decades ago, the concept keeps offering beautiful surprises. Recent theoretical research driven by new mathematical tools has proposed a remarkable dichotomy among the crucial strategies: successful individuals either act as partners or as rivals. Rivals strive for unilateral advantages by applying selfish or extortionate strategies. Partners aim to share the payoff for mutual cooperation, but are ready to fight back when being exploited. Which of these behaviours evolves depends on the environment. Whereas small population sizes and a limited number of rounds favour rivalry, partner strategies are selected when populations are large and relationships stable. Only partners allow for evolution of cooperation, while the rivals’ attempt to put themselves first leads to defection.

Suggested Citation

  • Christian Hilbe & Krishnendu Chatterjee & Martin A. Nowak, 2018. "Partners and rivals in direct reciprocity," Nature Human Behaviour, Nature, vol. 2(7), pages 469-477, July.
    • Handle: RePEc:nat:nathum:v:2:y:2018:i:7:d:10.1038_s41562-018-0320-9
    DOI: 10.1038/s41562-018-0320-9
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    Cited by:

    1. Wang, Bin & Kang, Wenjun & Sheng, Jinfang & Cheng, Lvhang & Hou, Zhengang, 2021. "Effects of trust-driven updating rule based on reputation in spatial prisoner’s dilemma games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 579(C).
    2. Masahiko Ueda & Toshiyuki Tanaka, 2020. "Linear algebraic structure of zero-determinant strategies in repeated games," PLOS ONE, Public Library of Science, vol. 15(4), pages 1-13, April.
    3. Laura Schmid & Farbod Ekbatani & Christian Hilbe & Krishnendu Chatterjee, 2023. "Quantitative assessment can stabilize indirect reciprocity under imperfect information," Nature Communications, Nature, vol. 14(1), pages 1-14, December.
    4. Shun Kurokawa & Joe Yuichiro Wakano & Yasuo Ihara, 2018. "Evolution of Groupwise Cooperation: Generosity, Paradoxical Behavior, and Non-Linear Payoff Functions," Games, MDPI, vol. 9(4), pages 1-24, December.
    5. Molnar, Grant & Hammond, Caroline & Fu, Feng, 2023. "Reactive means in the iterated Prisoner’s dilemma," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    6. Peter S. Park & Martin A. Nowak & Christian Hilbe, 2022. "Cooperation in alternating interactions with memory constraints," Nature Communications, Nature, vol. 13(1), pages 1-11, December.
    7. Kurokawa, Shun, 2019. "How memory cost, switching cost, and payoff non-linearity affect the evolution of persistence," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 174-192.
    8. 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.
    9. Johannes Wachs & J'anos Kert'esz, 2019. "A network approach to cartel detection in public auction markets," Papers 1906.08667, arXiv.org.
    10. Ma, Yin-Jie & Jiang, Zhi-Qiang & Podobnik, Boris, 2022. "Predictability of players’ actions as a mechanism to boost cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    11. Usui, Yuki & Ueda, Masahiko, 2021. "Symmetric equilibrium of multi-agent reinforcement learning in repeated prisoner’s dilemma," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    12. Xiaofeng Wang, 2021. "Costly Participation and The Evolution of Cooperation in the Repeated Public Goods Game," Dynamic Games and Applications, Springer, vol. 11(1), pages 161-183, March.
    13. Hahnel, Ulf J.J. & Fell, Michael J., 2022. "Pricing decisions in peer-to-peer and prosumer-centred electricity markets: Experimental analysis in Germany and the United Kingdom," Renewable and Sustainable Energy Reviews, Elsevier, vol. 162(C).
    14. Liu, Jinzhuo & Meng, Haoran & Wang, Wei & Xie, Zhongwen & Yu, Qian, 2019. "Evolution of cooperation on independent networks: The influence of asymmetric information sharing updating mechanism," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 234-241.
    15. Maria Kleshnina & Christian Hilbe & Štěpán Šimsa & Krishnendu Chatterjee & Martin A. Nowak, 2023. "The effect of environmental information on evolution of cooperation in stochastic games," Nature Communications, Nature, vol. 14(1), pages 1-11, December.
    16. Jia, Danyang & Li, Tong & Zhao, Yang & Zhang, Xiaoqin & Wang, Zhen, 2022. "Empty nodes affect conditional cooperation under reinforcement learning," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    17. Ding, Zhen-Wei & Zheng, Guo-Zhong & Cai, Chao-Ran & Cai, Wei-Ran & Chen, Li & Zhang, Ji-Qiang & Wang, Xu-Ming, 2023. "Emergence of cooperation in two-agent repeated games with reinforcement learning," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    18. Yohsuke Murase & Seung Ki Baek, 2021. "Friendly-rivalry solution to the iterated n-person public-goods game," PLOS Computational Biology, Public Library of Science, vol. 17(1), pages 1-17, January.

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