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On the stability of cooperation under indirect reciprocity with first-order information

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  • Berger, Ulrich
  • Grüne, Ansgar

Abstract

Indirect reciprocity describes a class of reputation-based mechanisms which may explain the prevalence of cooperation in large groups where partners meet only once. The first model for which this has been demonstrated was the image scoring mechanism. But analytical work on the simplest possible case, the binary scoring model, has shown that even small errors in implementation destabilize any cooperative regime. It has thus been claimed that for indirect reciprocity to stabilize cooperation, assessments of reputation must be based on higher-order information. Is indirect reciprocity relying on first-order information doomed to fail? We use a simple analytical model of image scoring to show that this need not be the case. Indeed, in the general image scoring model the introduction of implementation errors has just the opposite effect as in the binary scoring model: it may stabilize instead of destabilize cooperation.

Suggested Citation

  • Berger, Ulrich & Grüne, Ansgar, 2016. "On the stability of cooperation under indirect reciprocity with first-order information," Games and Economic Behavior, Elsevier, vol. 98(C), pages 19-33.
    • Handle: RePEc:eee:gamebe:v:98:y:2016:i:c:p:19-33
    DOI: 10.1016/j.geb.2016.05.003
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    Cited by:

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    2. Gaudeul, Alexia & Keser, Claudia & Müller, Stephan, 2021. "The evolution of morals under indirect reciprocity," Games and Economic Behavior, Elsevier, vol. 126(C), pages 251-277.
    3. Yuval Heller & Erik Mohlin, 2018. "Observations on Cooperation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(4), pages 2253-2282.
    4. Hopp, Daniel & Süß, Karolin, 2024. "How altruistic is indirect reciprocity? — Evidence from gift-exchange games in the lab," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 108(C).
    5. Wang, Chaoqian & Huang, Chaochao, 2022. "Between local and global strategy updating in public goods game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    6. Isamu Okada, 2020. "A Review of Theoretical Studies on Indirect Reciprocity," Games, MDPI, vol. 11(3), pages 1-17, July.
    7. 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.
    8. Christian Siemering, 2021. "The economics of dishonest insurance companies," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 46(1), pages 1-20, March.
    9. Zheng, Junjun & Ren, Tianyu & Ma, Gang & Dong, Jinhui, 2021. "The emergence and implementation of pool exclusion in spatial public goods game with heterogeneous ability-to-pay," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    10. Ingela Alger & Jörgen W. Weibull, 2017. "Strategic Behavior of Moralists and Altruists," Games, MDPI, vol. 8(3), pages 1-21, September.
    11. Quan, Ji & Nie, Jiacheng & Chen, Wenman & Wang, Xianjia, 2022. "Keeping or reversing social norms promote cooperation by enhancing indirect reciprocity," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    12. Lv, Ran & Qian, Jia-Li & Hao, Qing-Yi & Wu, Chao-Yun & Guo, Ning & Ling, Xiang, 2024. "The impact of reputation-based heterogeneous evaluation and learning on cooperation in spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).

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    More about this item

    Keywords

    Cooperation; Prisoner's dilemma; Donation game; Indirect reciprocity; Image scoring; First-order assessment; First-order information; Evolutionary stability;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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