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Tit-For-Tat Equilibria in Discounted Repeated Games with Private Monitoring

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  • Hitoshi Matsushima

    (Faculty of Economics, University of Tokyo)

Abstract

We investigate infinitely repeated games with imperfect private monitoring. We focus on a class of games where the payoff functions are additively separable and the signal for monitoring a player's action does not depend on the other player's action. Tit-for-tat strategies function very well in this class, according to which each player's action in each period depends only on the signal for the opponent's action one period before. With almost perfect monitoring, we show that even if the discount factors are fixed low, efficiency is approximated by a tit-for-tat Nash equilibrium payoff vector.

Suggested Citation

  • Hitoshi Matsushima, 2007. "Tit-For-Tat Equilibria in Discounted Repeated Games with Private Monitoring," CARF F-Series CARF-F-096, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    • Handle: RePEc:cfi:fseres:cf096
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    1. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
    2. 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.
    3. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, April.
    4. 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..
    5. 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.
    6. Sekiguchi, Tadashi, 1997. "Efficiency in Repeated Prisoner's Dilemma with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 76(2), pages 345-361, October.
    7. Piccione, Michele, 2002. "The Repeated Prisoner's Dilemma with Imperfect Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 70-83, January.
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