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Private Strategy and Efficiency: Repeated Partnership Games Revisited

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Author Info
Ichiro Obara (University of Pennsylvania)

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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.

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Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 1449.

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Date of creation: 01 Aug 2000
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Handle: RePEc:ecm:wc2000:1449

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Radner, Roy, 1986. "Repeated Partnership Games with Imperfect Monitoring and No Discounting," Review of Economic Studies, Blackwell Publishing, vol. 53(1), pages 43-57, January. [Downloadable!] (restricted)
  2. George J. Mailath & Stephen Morris, 1999. "Repeated Games with Almost-Public Monitoring," Cowles Foundation Discussion Papers 1236, Cowles Foundation, Yale University. [Downloadable!]
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  3. Jeffrey C. Ely & Juuso Valimaki, 1999. "A Robust Folk Theorem for the Prisoner's Dilemma," Discussion Papers 1264, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  4. Abreu, Dilip & Milgrom, Paul & Pearce, David, 1991. "Information and Timing in Repeated Partnerships," Econometrica, Econometric Society, vol. 59(6), pages 1713-33, November. [Downloadable!] (restricted)
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  5. Radner, Roy & Myerson, Roger & Maskin, Eric, 1986. "An Example of a Repeated Partnership Game with Discounting and with Uniformly Inefficient Equilibria," Review of Economic Studies, Blackwell Publishing, vol. 53(1), pages 59-69, January. [Downloadable!] (restricted)
  6. Drew Fudenberg & David K. Levine & Eric Maskin, 1994. "The Folk Theorem with Imperfect Public Information," Levine's Working Paper Archive 394, David K. Levine. [Downloadable!]
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  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. [Downloadable!] (restricted)
  8. Drew Fudenberg & David K Levine, 1999. "Efficiency and Observability with Long-Run and Short-Run Players," Levine's Working Paper Archive 81, David K. Levine. [Downloadable!]
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Ichiro Obara, . "Endogenous Monitoring," UCLA Economics Online Papers 398, UCLA Department of Economics. [Downloadable!]
    Other versions:
  2. 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. [Downloadable!]
  3. Hitoshi Matsushima, 2003. "Repeated Games with Private Monitoring: Two Players," CIRJE F-Series CIRJE-F-242, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
    Other versions:
  4. Michihiro Kandori & Ichiro Obara, 2004. "Efficiency in Repeated Games Revisited: The Role of Private Strategies," Levine's Bibliography 122247000000000055, UCLA Department of Economics. [Downloadable!]
    Other versions:
  5. V. Bhaskar & Ichiro Obara, . "Belief-Based Equilibria in the Repeated Prisoners' Dilemma with Private Monitoring," Penn CARESS Working Papers d93eb6f40c65728f9e1a7b114, Penn Economics Department. [Downloadable!]
    Other versions:
  6. Ichiro Obara, . "The Repeated Prisoner's Dilemma with Private Monitoring: a N-player case," CARESS Working Papres 99-13, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences. [Downloadable!]
    Other versions:
  7. 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. [Downloadable!]
  8. Stanley Reiter, 1999. "Coordination of Economic Activity: An Example," Discussion Papers 1263, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  9. Jeffrey C. Ely & Juuso Valimaki, 1999. "A Robust Folk Theorem for the Prisoner's Dilemma," Discussion Papers 1264, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
    Other versions:
  10. Andreas Blume & April Franco, 2002. "Learning from failure," Staff Report 299, Federal Reserve Bank of Minneapolis. [Downloadable!]
  11. Hitoshi Matsushima, 2001. "The Folk Theorem with Private Monitoring," CIRJE F-Series CIRJE-F-123, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
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