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Indirect Reciprocity with Optional Interactions and Private Information

Author

Listed:
  • Jason Olejarz

    (Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, MA 02138, USA
    These authors contributed equally to this work.)

  • Whan Ghang

    (Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, MA 02138, USA
    Department of Mathematics, Harvard University, One Oxford Street, Cambridge, MA 02138, USA
    National Institute for Mathematical Sciences, Daejeon 34047, Korea
    These authors contributed equally to this work.)

  • Martin A. Nowak

    (Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, MA 02138, USA
    Department of Mathematics, Harvard University, One Oxford Street, Cambridge, MA 02138, USA
    Department of Organismic and Evolutionary Biology, Harvard University, 26 Oxford Street, Cambridge, MA 02138, USA)

Abstract

We consider indirect reciprocity with optional interactions and private information. A game is offered between two players and accepted unless it is known that the other person is a defector. Whenever a defector manages to exploit a cooperator, his or her reputation is revealed to others in the population with some probability. Therefore, people have different private information about the reputation of others, which is a setting that is difficult to analyze in the theory of indirect reciprocity. Since a defector loses a fraction of his social ties each time he exploits a cooperator, he is less efficient at exploiting cooperators in subsequent rounds. We analytically calculate the critical benefit-to-cost ratio above which cooperation is successful in various settings. We demonstrate quantitative agreement with simulation results of a corresponding Wright–Fisher process with optional interactions and private information. We also deduce a simple necessary condition for the critical benefit-to-cost ratio.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jgames:v:6:y:2015:i:4:p:438-457:d:56667
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    References listed on IDEAS

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    1. 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.
    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. Bettina Rockenbach & Manfred Milinski, 2006. "The efficient interaction of indirect reciprocity and costly punishment," Nature, Nature, vol. 444(7120), pages 718-723, December.
    4. Martin A. Nowak & Karl Sigmund, 2005. "Evolution of indirect reciprocity," Nature, Nature, vol. 437(7063), pages 1291-1298, October.
    5. Martin A. Nowak & Akira Sasaki & Christine Taylor & Drew Fudenberg, 2004. "Emergence of cooperation and evolutionary stability in finite populations," Nature, Nature, vol. 428(6983), pages 646-650, April.
    6. Theodore C. Bergstrom, 2002. "Evolution of Social Behavior: Individual and Group Selection," Journal of Economic Perspectives, American Economic Association, vol. 16(2), pages 67-88, Spring.
    7. Bolton, Gary E. & Katok, Elena & Ockenfels, Axel, 2005. "Cooperation among strangers with limited information about reputation," Journal of Public Economics, Elsevier, vol. 89(8), pages 1457-1468, August.
    8. Hisashi Ohtsuki & Yoh Iwasa & Martin A. Nowak, 2009. "Indirect reciprocity provides only a narrow margin of efficiency for costly punishment," Nature, Nature, vol. 457(7225), pages 79-82, January.
    9. Seinen, Ingrid & Schram, Arthur, 2006. "Social status and group norms: Indirect reciprocity in a repeated helping experiment," European Economic Review, Elsevier, vol. 50(3), pages 581-602, April.
    10. Michihiro Kandori, 1992. "Social Norms and Community Enforcement," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(1), pages 63-80.
    11. Berger, Ulrich, 2011. "Learning to cooperate via indirect reciprocity," Games and Economic Behavior, Elsevier, vol. 72(1), pages 30-37, May.
    12. Mitsuhiro Nakamura & Naoki Masuda, 2011. "Indirect Reciprocity under Incomplete Observation," PLOS Computational Biology, Public Library of Science, vol. 7(7), pages 1-10, July.
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    Cited by:

    1. Christian Hilbe & Moshe Hoffman & Martin A. Nowak, 2015. "Cooperate without Looking in a Non-Repeated Game," Games, MDPI, vol. 6(4), pages 1-15, September.
    2. 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.
    3. Tatsuya Sasaki & Hitoshi Yamamoto & Isamu Okada & Satoshi Uchida, 2017. "The Evolution of Reputation-Based Cooperation in Regular Networks," Games, MDPI, vol. 8(1), pages 1-16, January.
    4. Liang, Rizhou & Zhang, Jiqiang & Zheng, Guozhong & Chen, Li, 2021. "Social hierarchy promotes the cooperation prevalence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    5. 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.
    6. Isamu Okada, 2020. "A Review of Theoretical Studies on Indirect Reciprocity," Games, MDPI, vol. 11(3), pages 1-17, July.
    7. Mike Farjam & Wladislaw Mill & Marian Panganiban, 2016. "Ignorance Is Bliss, But for Whom? The Persistent Effect of Good Will on Cooperation," Games, MDPI, vol. 7(4), pages 1-19, October.
    8. Tadeas Priklopil & Krishnendu Chatterjee, 2015. "Evolution of Decisions in Population Games with Sequentially Searching Individuals," Games, MDPI, vol. 6(4), pages 1-25, September.

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