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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.

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Bibliographic Info

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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  1. George J Mailath & Stephen Morris, 1999. "Repeated Games with Almost Public Monitoring," Levine's Working Paper Archive 2107, David K. Levine.
  2. David G. Pearce & Dilip Abreu & Paul R. Milgrom, 1988. "Information and Timing in Repeated Partnerships," Cowles Foundation Discussion Papers 875, Cowles Foundation for Research in Economics, Yale University.
  3. Drew Fudenberg & David K. Levine & Eric Maskin, 1994. "The Folk Theorem with Imperfect Public Information," Levine's Working Paper Archive 394, David K. Levine.
  4. Piccione, Michele, 2002. "The Repeated Prisoner's Dilemma with Imperfect Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 70-83, January.
  5. Jeffrey Ely, 2000. "A Robust Folk Theorem for the Prisoners' Dilemma," Econometric Society World Congress 2000 Contributed Papers 0210, Econometric Society.
  6. Radner, Roy, 1986. "Repeated Partnership Games with Imperfect Monitoring and No Discounting," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 43-57, January.
  7. 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, Wiley Blackwell, vol. 53(1), pages 59-69, January.
  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.
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Cited by:
  1. Michihiro Kandori & Ichiro Obara, 2004. "Endogeous Monitoring," 2004 Meeting Papers 752, Society for Economic Dynamics.
  2. 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.
  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. Michihiro Kandori & Ichiro Obara, 2003. "Efficiency in Repeated Games Revisited: The Role of Private Strategies," CIRJE F-Series CIRJE-F-255, CIRJE, Faculty of Economics, University of Tokyo.
  5. 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.
  6. V. Bhaskar & Ichiro Obara, 2000. "Belief-Based Equilibria in the Repeated Prisoners' Dilemma with Private Monitoring," Econometric Society World Congress 2000 Contributed Papers 1330, Econometric Society.
  7. Stanley Reiter, 1999. "Coordination of Economic Activity: An Example," Discussion Papers 1263, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. Andreas Blume & April Franco, 2002. "Learning from failure," Staff Report 299, Federal Reserve Bank of Minneapolis.

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