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Private Strategy and Efficiency: Repeated Partnership Games Revisited

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  • Ichiro Obara

    (University of Pennsylvania)

Abstract

This paper studies repeated partnership games with only two public signals, the game studied in Radner Myerson and Maskin(1986) except that the stage game is discrete. It is well known that the public perfect equilibrium (PPE) payoff set is bounded away from the efficient frontier in this class of game. However, it has not been unanswered how this restriction to public strategies is restrictive even in this simple class of repeated games. In this paper, I construct a strongly symmetric sequential equilibrium whose payoff dominates the best symmetric PPE payoff. The strategy used to construct this equilibrium depends not only on public signals but also on player's own past actions. I call this kind of strategy private strategy and such an equilibrium a private sequential equilibrium. I also provide an example where the private sequential equilibrium approximates the efficient outcome, but the PPE payoff set is contained in an arbitrary small neighborhood of the stage game Nash equilibrium payoff. In precise, I can find a sequence of the stage game (partnership game) where the private strategy sequential equilibrium converges to the symmetric efficient outcome and the whole PPE payoff set converges to the stage game Nash equilibrium payoff. This implies that the private sequential equilibrium payoff dominates any PPE payoff. This example suggests that the difference between a PPE payoff set and a sequential equilibrium payoff set can be potentially significant.

Suggested Citation

  • Ichiro Obara, 2000. "Private Strategy and Efficiency: Repeated Partnership Games Revisited," Econometric Society World Congress 2000 Contributed Papers 1449, Econometric Society.
  • Handle: RePEc:ecm:wc2000:1449
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    References listed on IDEAS

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    1. Mailath, George J. & Morris, Stephen, 2002. "Repeated Games with Almost-Public Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 189-228, January.
    2. Fudenberg Drew & Levine David K., 1994. "Efficiency and Observability with Long-Run and Short-Run Players," Journal of Economic Theory, Elsevier, vol. 62(1), pages 103-135, February.
    3. 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.
    4. Fudenberg, Drew & Levine, David I & Maskin, Eric, 1994. "The Folk Theorem with Imperfect Public Information," Econometrica, Econometric Society, vol. 62(5), pages 997-1039, September.
    5. Abreu, Dilip & Milgrom, Paul & Pearce, David, 1991. "Information and Timing in Repeated Partnerships," Econometrica, Econometric Society, vol. 59(6), pages 1713-1733, November.
    6. Roy Radner, 1986. "Repeated Partnership Games with Imperfect Monitoring and No Discounting," Review of Economic Studies, Oxford University Press, vol. 53(1), pages 43-57.
    7. Roy Radner & Roger Myerson & Eric Maskin, 1986. "An Example of a Repeated Partnership Game with Discounting and with Uniformly Inefficient Equilibria," Review of Economic Studies, Oxford University Press, vol. 53(1), pages 59-69.
    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.
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    Cited by:

    1. Hitoshi Matsushima, 2002. "Repeated Games with Correlated Private Monitoring and Secret Price Cuts," CIRJE F-Series CIRJE-F-154, CIRJE, Faculty of Economics, University of Tokyo.
    2. Michihiro Kandori, 2011. "Weakly Belief‐Free Equilibria in Repeated Games With Private Monitoring," Econometrica, Econometric Society, vol. 79(3), pages 877-892, May.
    3. Ichiro Obara, "undated". "The Repeated Prisoner's Dilemma with Private Monitoring: a N-player case," Penn CARESS Working Papers ba7f35f1c50de4503e241d127, Penn Economics Department.
    4. Ichiro Obara, 2004. "Efficiency in Repeated Games Revisited: The Role of Private Strategies (with M. Kandori)," UCLA Economics Online Papers 281, UCLA Department of Economics.
    5. Ichiro Obara, "undated". "Endogenous Monitoring," UCLA Economics Online Papers 398, UCLA Department of Economics.
    6. Andreas Blume & April Franco, 2002. "Learning from failure," Staff Report 299, Federal Reserve Bank of Minneapolis.
    7. 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.
    8. Michihiro Kandori & Ichiro Obara, 2006. "Efficiency in Repeated Games Revisited: The Role of Private Strategies," Econometrica, Econometric Society, vol. 74(2), pages 499-519, March.
    9. Stanley Reiter, 1999. "Coordination of Economic Activity: An Example," Discussion Papers 1263, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    10. Bhaskar, V. & Obara, Ichiro, 2002. "Belief-Based Equilibria in the Repeated Prisoners' Dilemma with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 40-69, January.
    11. Sekiguchi, Tadashi, 2001. "A negative result in finitely repeated games with product monitoring," Economics Letters, Elsevier, vol. 74(1), pages 67-70, December.

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