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Interlinkage and Generous Tit-for-Tat Strategy

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  • Hitoshi Matsushima

Abstract

type="main"> We investigate an infinitely-repeated prisoners' dilemma with imperfect monitoring and consider the possibility that the interlinkage of the players' distinct activities enhances implicit collusion. We show a necessary and sufficient condition for the existence of a generous tit-for-tat Nash equilibrium. Such an equilibrium, if it exists, is unique. This equilibrium achieves approximate efficiency when monitoring is almost perfect, where the discount factors are fixed.

Suggested Citation

  • Hitoshi Matsushima, 2014. "Interlinkage and Generous Tit-for-Tat Strategy," The Japanese Economic Review, Japanese Economic Association, vol. 65(1), pages 116-121, March.
    • Handle: RePEc:bla:jecrev:v:65:y:2014:i:1:p:116-121
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    File URL: http://hdl.handle.net/10.1111/jere.12014
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    1. 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.
    2. Matsushima, Hitoshi, 1991. "On the theory of repeated games with private information : Part I: anti-folk theorem without communication," Economics Letters, Elsevier, vol. 35(3), pages 253-256, March.
    3. Sekiguchi, Tadashi, 1997. "Efficiency in Repeated Prisoner's Dilemma with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 76(2), pages 345-361, October.
    4. Matsushima, Hitoshi, 1991. "On the theory of repeated games with private information : Part II: revelation through communication," Economics Letters, Elsevier, vol. 35(3), pages 257-261, March.
    5. Piccione, Michele, 2002. "The Repeated Prisoner's Dilemma with Imperfect Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 70-83, January.
    6. Hitoshi Matsushima, 2004. "Repeated Games with Private Monitoring: Two Players," Econometrica, Econometric Society, vol. 72(3), pages 823-852, May.
    7. Takahashi, Satoru, 2010. "Community enforcement when players observe partners' past play," Journal of Economic Theory, Elsevier, vol. 145(1), pages 42-62, January.
    8. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Obayashi Shinya & Inagaki Yusuke & Takikawa Hiroki, 2016. "The Condition for Generous Trust," PLOS ONE, Public Library of Science, vol. 11(11), pages 1-16, November.
    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. 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.
    7. 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.
    8. 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.
    9. 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.

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