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Hybrid Assessment Scheme Based on the Stern- Judging Rule for Maintaining Cooperation under Indirect Reciprocity

Author

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  • Isamu Okada

    (Faculty of Business Administration, Soka University, Tangi 1-236, Hachioji City, Tokyo 192-8577, Japan
    Department of Information Systems and Operations, Vienna University of Economics, 1020 Wien, Austria)

  • Hitoshi Yamamoto

    (Department of Information Systems and Operations, Vienna University of Economics, 1020 Wien, Austria
    Faculty of Business Administration, Rissho University, Shinagawa City, Tokyo 141-8602, Japan)

  • Satoshi Uchida

    (Research Center for Ethi-Culture Studies, RINRI Institute, Chiyoda City, Tokyo 102-8561, Japan)

Abstract

Intensive studies on indirect reciprocity have explored rational assessment rules for maintaining cooperation and several have demonstrated the effects of the stern-judging rule. Uchida and Sasaki demonstrated that the stern-judging rule is not suitable for maintaining cooperative regimes in private assessment conditions while a public assessment system has been assumed in most studies. Although both assessment systems are oversimplified and society is most accurately represented by a mixture of these systems, little analysis has been reported on their mixture. Here, we investigated how much weight on the use of information originating from a public source is needed to maintain cooperative regimes for players adopting the stern-judging rule when players get information from both public and private sources. We did this by considering a hybrid-assessment scheme in which players use both assessment systems and by using evolutionary game theory. We calculated replicator equations using the expected payoffs of three strategies: unconditional cooperation, unconditional defection, and stern-judging rule adoption. Our analysis shows that the use of the rule helps to maintain cooperation if reputation information from a unique public notice board is used with more than a threshold probability. This hybrid-assessment scheme can be applied to other rules, including the simple-standing rule and the staying rule.

Suggested Citation

  • Isamu Okada & Hitoshi Yamamoto & Satoshi Uchida, 2020. "Hybrid Assessment Scheme Based on the Stern- Judging Rule for Maintaining Cooperation under Indirect Reciprocity," Games, MDPI, vol. 11(1), pages 1-10, February.
    • Handle: RePEc:gam:jgames:v:11:y:2020:i:1:p:13-:d:323209
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    References listed on IDEAS

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    1. Karthik Panchanathan & Robert Boyd, 2004. "Indirect reciprocity can stabilize cooperation without the second-order free rider problem," Nature, Nature, vol. 432(7016), pages 499-502, November.
    2. Kandori, Michihiro, 2002. "Introduction to Repeated Games with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 1-15, January.
    3. Uchida, Satoshi & Sasaki, Tatsuya, 2013. "Effect of assessment error and private information on stern-judging in indirect reciprocity," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 175-180.
    4. U. Dieckmann & R. Law, 1996. "The Dynamical Theory of Coevolution: A Derivation from Stochastic Ecological Processes," Working Papers wp96001, International Institute for Applied Systems Analysis.
    5. Jason Olejarz & Whan Ghang & Martin A. Nowak, 2015. "Indirect Reciprocity with Optional Interactions and Private Information," Games, MDPI, vol. 6(4), pages 1-20, September.
    6. Christian Hilbe & Laura Schmid & Josef Tkadlec & Krishnendu Chatterjee & Martin A. Nowak, 2018. "Indirect reciprocity with private, noisy, and incomplete information," Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, vol. 115(48), pages 12241-12246, November.
    7. Martin A. Nowak & Karl Sigmund, 1998. "Evolution of indirect reciprocity by image scoring," Nature, Nature, vol. 393(6685), pages 573-577, June.
    8. M.A. Nowak & K. Sigmund, 1998. "Evolution of Indirect Reciprocity by Image Scoring/ The Dynamics of Indirect Reciprocity," Working Papers ir98040, International Institute for Applied Systems Analysis.
    9. Bettina Rockenbach & Manfred Milinski, 2006. "The efficient interaction of indirect reciprocity and costly punishment," Nature, Nature, vol. 444(7120), pages 718-723, December.
    10. Martin A. Nowak & Karl Sigmund, 2005. "Evolution of indirect reciprocity," Nature, Nature, vol. 437(7063), pages 1291-1298, October.
    11. John M. McNamara & Polly Doodson, 2015. "Reputation can enhance or suppress cooperation through positive feedback," Nature Communications, Nature, vol. 6(1), pages 1-7, May.
    12. Misato Inaba & Nobuyuki Takahashi, 2019. "Linkage Based on the Kandori Norm Successfully Sustains Cooperation in Social Dilemmas," Games, MDPI, vol. 10(1), pages 1-15, February.
    13. Michihiro Kandori, 1992. "Social Norms and Community Enforcement," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(1), pages 63-80.
    14. Hisashi Ohtsuki & Yoh Iwasa & Martin A Nowak, 2015. "Reputation Effects in Public and Private Interactions," PLOS Computational Biology, Public Library of Science, vol. 11(11), pages 1-11, November.
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    1. Isamu Okada, 2020. "A Review of Theoretical Studies on Indirect Reciprocity," Games, MDPI, vol. 11(3), pages 1-17, July.

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