IDEAS home Printed from https://ideas.repec.org/p/tky/fseres/2016cf1004.html
   My bibliography  Save this paper

Accuracy and Retaliation in Repeated Games with Imperfect Private Monitoring:Experiments and Theory

Author

Listed:
  • Yutaka Kayaba

    (Hitotsubashi Institute for Advanced Study, Hitotsubashi University)

  • Hitoshi Matsushima

    (Faculty of Economics, The University of Tokyo)

  • Tomohisa Toyama

    (Division of Liberal Arts, Kogakuin University)

Abstract

We experimentally examine repeated prisoners' dilemma with random termination, where monitoring is imperfect and private. Our estimation indicates that a significant proportion of subjects follow generous Tit-For-Tat (g-TFT) strategies, straightforward extensions of Tit-For-Tat. However, the observed retaliating policies are inconsistent with the g-TFT equilibria. Contrarily to the theory, subjects tend to retaliate more with high accuracy than with low accuracy. They tend to retaliate more than the theory predicts with high accuracy, while they tend to retaliate lesser with low accuracy. In order to describe these results as unique equilibrium, we demonstrate an alternative theory that incorporates naïveté and reciprocity.

Suggested Citation

  • Yutaka Kayaba & Hitoshi Matsushima & Tomohisa Toyama, 2016. "Accuracy and Retaliation in Repeated Games with Imperfect Private Monitoring:Experiments and Theory," CIRJE F-Series CIRJE-F-1004, CIRJE, Faculty of Economics, University of Tokyo.
  • Handle: RePEc:tky:fseres:2016cf1004
    as

    Download full text from publisher

    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2016/2016cf1004.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ernst Fehr & Simon Gächter, 2000. "Fairness and Retaliation: The Economics of Reciprocity," Journal of Economic Perspectives, American Economic Association, vol. 14(3), pages 159-181, Summer.
    2. Masaki Aoyagi & V. Bhaskar & Guillaume R. Fréchette, 2019. "The Impact of Monitoring in Infinitely Repeated Games: Perfect, Public, and Private," American Economic Journal: Microeconomics, American Economic Association, vol. 11(1), pages 1-43, February.
    3. 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..
    4. Drew Fudenberg & Eric Maskin, 2008. "The Folk Theorem In Repeated Games With Discounting Or With Incomplete Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 11, pages 209-230, World Scientific Publishing Co. Pte. Ltd..
    5. Hitoshi Matsushima & Tomomi Tanaka & Tomohisa Toyama, 2013. "Behavioral Approach to Repeated Games with Private Monitoring," CIRJE F-Series CIRJE-F-879, CIRJE, Faculty of Economics, University of Tokyo.
    6. Urs Fischbacher, 2007. "z-Tree: Zurich toolbox for ready-made economic experiments," Experimental Economics, Springer;Economic Science Association, vol. 10(2), pages 171-178, June.
    7. Hitoshi Matsushima, 2014. "Interlinkage and Generous Tit-for-Tat Strategy," The Japanese Economic Review, Japanese Economic Association, vol. 65(1), pages 116-121, March.
    8. 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.
    9. Hitoshi Matsushima, 2004. "Repeated Games with Private Monitoring: Two Players," Econometrica, Econometric Society, vol. 72(3), pages 823-852, May.
    10. Takahashi, Satoru, 2010. "Community enforcement when players observe partners' past play," Journal of Economic Theory, Elsevier, vol. 145(1), pages 42-62, January.
    11. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1990. "Toward a Theory of Discounted Repeated Games with Imperfect Monitoring," Econometrica, Econometric Society, vol. 58(5), pages 1041-1063, September.
    12. Green, Edward J & Porter, Robert H, 1984. "Noncooperative Collusion under Imperfect Price Information," Econometrica, Econometric Society, vol. 52(1), pages 87-100, January.
    13. Pedro Dal Bo & Guillaume R. Frochette, 2011. "The Evolution of Cooperation in Infinitely Repeated Games: Experimental Evidence," American Economic Review, American Economic Association, vol. 101(1), pages 411-429, February.
    14. Yves Breitmoser, 2015. "Cooperation, but No Reciprocity: Individual Strategies in the Repeated Prisoner's Dilemma," American Economic Review, American Economic Association, vol. 105(9), pages 2882-2910, September.
    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. Berg Joyce & Dickhaut John & McCabe Kevin, 1995. "Trust, Reciprocity, and Social History," Games and Economic Behavior, Elsevier, vol. 10(1), pages 122-142, July.
    17. John Duffy & Félix Muñoz-García, 2012. "Patience or Fairness? Analyzing Social Preferences in Repeated Games," Games, MDPI, vol. 3(1), pages 1-22, March.
    18. 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.
    19. Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-396, March.
    20. Roy Radner, 1986. "Repeated Partnership Games with Imperfect Monitoring and No Discounting," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 43-57.
    21. Piccione, Michele, 2002. "The Repeated Prisoner's Dilemma with Imperfect Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 70-83, January.
    22. Pedro Dal Bó, 2005. "Cooperation under the Shadow of the Future: Experimental Evidence from Infinitely Repeated Games," American Economic Review, American Economic Association, vol. 95(5), pages 1591-1604, December.
    23. 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.
    24. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
    25. McKelvey, Richard D. & Palfrey, Thomas R., 2008. "Quantal Response Equilibria: A Brief Synopsis," Handbook of Experimental Economics Results, in: Charles R. Plott & Vernon L. Smith (ed.), Handbook of Experimental Economics Results, edition 1, volume 1, chapter 60, pages 541-548, Elsevier.
    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. Gallo, Edoardo & Riyanto, Yohanes E. & Roy, Nilanjan & Teh, Tat-How, 2019. "Cooperation in an Uncertain and Dynamic World," MPRA Paper 97878, University Library of Munich, Germany.

    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. 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.
    2. 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.
    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.
    4. Matsushima Hitoshi, 2020. "Behavioral Theory of Repeated Prisoner’s Dilemma: Generous Tit-For-Tat Strategy," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 20(1), pages 1-11, January.
    5. 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.
    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. 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.
    8. Hitoshi Matsushima & Tomomi Tanaka & Tomohisa Toyama, 2013. "Behavioral Approach to Repeated Games with Private Monitoring," CIRJE F-Series CIRJE-F-879, CIRJE, Faculty of Economics, University of Tokyo.
    9. Rand, David G. & Fudenberg, Drew & Dreber, Anna, 2015. "It's the thought that counts: The role of intentions in noisy repeated games," Journal of Economic Behavior & Organization, Elsevier, vol. 116(C), pages 481-499.
    10. 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.
    11. Jehiel, Philippe & Samuelson, Larry, 2023. "The analogical foundations of cooperation," Journal of Economic Theory, Elsevier, vol. 208(C).
    12. Tomala, Tristan, 2009. "Perfect communication equilibria in repeated games with imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 67(2), pages 682-694, November.
    13. 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.
    14. Heller, Yuval, 2017. "Instability of belief-free equilibria," Journal of Economic Theory, Elsevier, vol. 168(C), pages 261-286.
    15. Kandori, Michihiro, 2002. "Introduction to Repeated Games with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 1-15, January.
    16. Chen, Bo, 2010. "A belief-based approach to the repeated prisoners' dilemma with asymmetric private monitoring," Journal of Economic Theory, Elsevier, vol. 145(1), pages 402-420, January.
    17. Wilson, Alistair J. & Wu, Hong, 2017. "At-will relationships: How an option to walk away affects cooperation and efficiency," Games and Economic Behavior, Elsevier, vol. 102(C), pages 487-507.
    18. , J. & ,, 2006. "Coordination failure in repeated games with almost-public monitoring," Theoretical Economics, Econometric Society, vol. 1(3), pages 311-340, September.
    19. Mailath, George J. & Olszewski, Wojciech, 2011. "Folk theorems with bounded recall under (almost) perfect monitoring," Games and Economic Behavior, Elsevier, vol. 71(1), pages 174-192, January.
    20. Michihiro Kandori, 2011. "Weakly Belief‐Free Equilibria in Repeated Games With Private Monitoring," Econometrica, Econometric Society, vol. 79(3), pages 877-892, May.

    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:2016cf1004. 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.