IDEAS home Printed from https://ideas.repec.org/p/tky/fseres/2019cf1115.html
   My bibliography  Save this paper

Behavioral Theory of Repeated Prisoner's Dilemma: Generous Tit-For-Tat Strategy

Author

Listed:
  • Hitoshi Matsushima

    (Faculty of Economics, The University of Tokyo)

Abstract

This study investigates infinitely repeated games of a prisoner's dilemma with additive separability in which the monitoring technology is imperfect and private. Behavioral incentives indicate that, in this setting, a player is not only motivated by pure self-interest but also by reciprocity. Players often become naive and select an action unconsciously. By focusing on generous tit-for-tat strategies, we characterize a Nash equilibrium with behavioral incentives, termed behavioral equilibrium, in an accuracy-contingent manner. By eliminating the gap between theory and evidence, this study argues that reciprocity plays a substantial role in motivating a player to consciously make decisions.

Suggested Citation

  • Hitoshi Matsushima, 2019. "Behavioral Theory of Repeated Prisoner's Dilemma: Generous Tit-For-Tat Strategy," CIRJE F-Series CIRJE-F-1115, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2019cf1115
    as

    Download full text from publisher

    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2019/2019cf1115.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Gary Charness & Matthew Rabin, 2002. "Understanding Social Preferences with Simple Tests," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(3), pages 817-869.
    2. Hitoshi Matsushima, 2014. "Interlinkage and Generous Tit-for-Tat Strategy," The Japanese Economic Review, Japanese Economic Association, vol. 65(1), pages 116-121, March.
    3. Green, Edward J & Porter, Robert H, 1984. "Noncooperative Collusion under Imperfect Price Information," Econometrica, Econometric Society, vol. 52(1), pages 87-100, January.
    4. John Duffy & Félix Muñoz-García, 2012. "Patience or Fairness? Analyzing Social Preferences in Repeated Games," Games, MDPI, vol. 3(1), pages 1-22, March.
    5. Ely, Jeffrey C. & Valimaki, Juuso, 2002. "A Robust Folk Theorem for the Prisoner's Dilemma," Journal of Economic Theory, Elsevier, vol. 102(1), pages 84-105, January.
    6. Drew Fudenberg & David Levine & Eric Maskin, 2008. "The Folk Theorem With Imperfect Public Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 12, pages 231-273, World Scientific Publishing Co. Pte. Ltd..
    7. Kayaba, Yutaka & Matsushima, Hitoshi & Toyama, Tomohisa, 2020. "Accuracy and retaliation in repeated games with imperfect private monitoring: Experiments," Games and Economic Behavior, Elsevier, vol. 120(C), pages 193-208.
    8. Piccione, Michele, 2002. "The Repeated Prisoner's Dilemma with Imperfect Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 70-83, January.
    9. Drew Fudenberg & David G. Rand & Anna Dreber, 2012. "Slow to Anger and Fast to Forgive: Cooperation in an Uncertain World," American Economic Review, American Economic Association, vol. 102(2), pages 720-749, April.
    10. Hitoshi Matsushima, 2004. "Repeated Games with Private Monitoring: Two Players," Econometrica, Econometric Society, vol. 72(3), pages 823-852, May.
    11. Takahashi, Satoru, 2010. "Community enforcement when players observe partners' past play," Journal of Economic Theory, Elsevier, vol. 145(1), pages 42-62, January.
    12. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
    13. Rabin, Matthew, 1993. "Incorporating Fairness into Game Theory and Economics," American Economic Review, American Economic Association, vol. 83(5), pages 1281-1302, December.
    14. Per Molander, 1985. "The Optimal Level of Generosity in a Selfish, Uncertain Environment," Journal of Conflict Resolution, Peace Science Society (International), vol. 29(4), pages 611-618, December.
    15. Guth, Werner & Schmittberger, Rolf & Schwarze, Bernd, 1982. "An experimental analysis of ultimatum bargaining," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 367-388, December.
    16. Yutaka Kayaba & Hitoshi Matsushima & Tomohisa Toyama, 2019. "Accuracy and Retaliation in Repeated Games with Imperfect Private Monitoring: Experiments (Revised version of CARF-F-433)," CARF F-Series CARF-F-466, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    17. Berg Joyce & Dickhaut John & McCabe Kevin, 1995. "Trust, Reciprocity, and Social History," Games and Economic Behavior, Elsevier, vol. 10(1), pages 122-142, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kayaba, Yutaka & Matsushima, Hitoshi & Toyama, Tomohisa, 2020. "Accuracy and retaliation in repeated games with imperfect private monitoring: Experiments," Games and Economic Behavior, Elsevier, vol. 120(C), pages 193-208.
    2. Yao, Zhouzhou & Wu, Xianyu & Yang, Yang & Li, Ning, 2024. "A digital decision approach for indirect-reciprocity based cooperative lane-changing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
    3. Yutaka Kayaba & Hitoshi Matsushima & Tomohisa Toyama, 2019. "Accuracy and Retaliation in Repeated Games with Imperfect Private Monitoring: Experiments (Revised version of CARF-F-433)," CARF F-Series CARF-F-466, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hitoshi Matsushima, 2019. "Behavioral Theory of Repeated Prisoner’s Dilemma: Generous Tit-For-Tat Strategy (Forthcoming in the B. E. Journal of Theoretical Economics)," CARF F-Series CARF-F-452, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. Yutaka Kayaba & Hitoshi Matsushima & Tomohisa Toyama, 2017. "Accuracy and Retaliation in Repeated Games with Imperfect Private Monitoring: Experiments and Theory (Revised version of F-381)," CARF F-Series CARF-F-414, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    3. Yutaka Kayaba & Hitoshi Matsushima & Tomohisa Toyama, 2016. "Accuracy and Retaliation in Repeated Games with Imperfect Private Monitoring: Experiments and Theory," CARF F-Series CARF-F-381, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    4. Yutaka Kayaba & Hitoshi Matsushima & Tomohisa Toyama, 2019. "Accuracy and Retaliation in Repeated Games with Imperfect Private Monitoring: Experiments (Revised version of CARF-F-433)," CARF F-Series CARF-F-466, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    5. Kayaba, Yutaka & Matsushima, Hitoshi & Toyama, Tomohisa, 2020. "Accuracy and retaliation in repeated games with imperfect private monitoring: Experiments," Games and Economic Behavior, Elsevier, vol. 120(C), pages 193-208.
    6. Hitoshi Matsushima & Tomohisa Toyama, 2011. "Monitoring Accuracy and Retaliation in Infinitely Repeated Games with Imperfect Private Monitoring: Theory and Experiments," CIRJE F-Series CIRJE-F-795, CIRJE, Faculty of Economics, University of Tokyo.
    7. Hitoshi Matsushima & Tomomi Tanaka & Tomohisa Toyama, 2013. "Behavioral Approach to Repeated Games with Private Monitoring," CARF F-Series CARF-F-309, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    8. Yuichi Yamamoto, 2013. "Individual Learning and Cooperation in Noisy Repeated Games," PIER Working Paper Archive 13-038, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    9. Yuichi Yamamoto, 2012. "Individual Learning and Cooperation in Noisy Repeated Games," PIER Working Paper Archive 12-044, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    10. Miyagawa, Eiichi & Miyahara, Yasuyuki & Sekiguchi, Tadashi, 2008. "The folk theorem for repeated games with observation costs," Journal of Economic Theory, Elsevier, vol. 139(1), pages 192-221, March.
    11. , H. & ,, 2016. "Approximate efficiency in repeated games with side-payments and correlated signals," Theoretical Economics, Econometric Society, vol. 11(1), January.
    12. Yamamoto, Yuichi, 2012. "Characterizing belief-free review-strategy equilibrium payoffs under conditional independence," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1998-2027.
    13. Fabian Dvorak & Sebastian Fehrler, 2024. "Negotiating Cooperation under Uncertainty: Communication in Noisy, Indefinitely Repeated Interactions," American Economic Journal: Microeconomics, American Economic Association, vol. 16(3), pages 232-258, August.
    14. Yamamoto, Yuichi, 2009. "A limit characterization of belief-free equilibrium payoffs in repeated games," Journal of Economic Theory, Elsevier, vol. 144(2), pages 802-824, March.
    15. , J. & ,, 2006. "Coordination failure in repeated games with almost-public monitoring," Theoretical Economics, Econometric Society, vol. 1(3), pages 311-340, September.
    16. Carmona, Guilherme & Laohakunakorn, Krittanai, 2023. "The folk theorem for the prisoner's dilemma with endogenous private monitoring," Journal of Economic Theory, Elsevier, vol. 213(C).
    17. Heller, Yuval, 2017. "Instability of belief-free equilibria," Journal of Economic Theory, Elsevier, vol. 168(C), pages 261-286.
    18. Tomala, Tristan, 2009. "Perfect communication equilibria in repeated games with imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 67(2), pages 682-694, November.
    19. Johannes Hörner & Julian Jamison, 2007. "Collusion with (almost) no information," RAND Journal of Economics, RAND Corporation, vol. 38(3), pages 804-822, September.
    20. Sugaya, Takuo & Yamamoto, Yuichi, 2020. "Common learning and cooperation in repeated games," Theoretical Economics, Econometric Society, vol. 15(3), July.

    More about this item

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tky:fseres:2019cf1115. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CIRJE administrative office (email available below). General contact details of provider: https://edirc.repec.org/data/ritokjp.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.