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Evolutionary stability of first-order-information indirect reciprocity in sizable groups

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  • Suzuki, Shinsuke
  • Akiyama, Eizo

Abstract

Indirect reciprocity is considered as a key mechanism for explaining the evolution of cooperation in situations where the same individuals interact only a few times. Under indirect reciprocity, an individual who helps others gets returns indirectly from others who know her good reputation. Recently, many studies have discussed the effect of reputation criteria based only on the former actions of the others (first-order information) and of those based also on the former reputation of opponents of the others (second-order information) on the evolution of indirect reciprocity. In this study, we investigate the evolutionary stability of the indirectly reciprocal strategy (discriminating strategy: DIS), which cooperates only with opponents who have good reputations, in n(>2)-person games where more than two individuals take part in a single group (interaction). We show that in n-person games, DIS is an evolutionarily stable strategy (ESS) even under the image-scoring reputation criterion, which is based only on first-order information and where cooperations (defections) are judged to be good (bad). This result is in contrast to that of 2-person games where DIS is not an ESS under reputation criteria based only on first-order information.

Suggested Citation

  • Suzuki, Shinsuke & Akiyama, Eizo, 2008. "Evolutionary stability of first-order-information indirect reciprocity in sizable groups," Theoretical Population Biology, Elsevier, vol. 73(3), pages 426-436.
    • Handle: RePEc:eee:thpobi:v:73:y:2008:i:3:p:426-436
    DOI: 10.1016/j.tpb.2007.12.005
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    References listed on IDEAS

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    1. Martin A. Nowak & Karl Sigmund, 1998. "Evolution of indirect reciprocity by image scoring," Nature, Nature, vol. 393(6685), pages 573-577, June.
    2. 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.
    3. Martin A. Nowak & Karl Sigmund, 2005. "Evolution of indirect reciprocity," Nature, Nature, vol. 437(7063), pages 1291-1298, October.
    4. 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.
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    Cited by:

    1. Xinrong Yang & Zhenping Geng & Haitao Li, 2023. "Matrix-Based Method for the Analysis and Control of Networked Evolutionary Games: A Survey," Games, MDPI, vol. 14(2), pages 1-13, February.
    2. Kurokawa, Shun & Wakano, Joe Yuichiro & Ihara, Yasuo, 2010. "Generous cooperators can outperform non-generous cooperators when replacing a population of defectors," Theoretical Population Biology, Elsevier, vol. 77(4), pages 257-262.
    3. 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.
    4. Berger Ulrich & Ansgar Grüne, 2014. "Evolutionary Stability of Indirect Reciprocity by Image Scoring," Department of Economics Working Papers wuwp168, Vienna University of Economics and Business, Department of Economics.
    5. Genki Ichinose & Masaya Saito & Shinsuke Suzuki, 2013. "Collective Chasing Behavior between Cooperators and Defectors in the Spatial Prisoner’s Dilemma," PLOS ONE, Public Library of Science, vol. 8(7), pages 1-10, July.

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