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Repeated Games with Correlated Private Monitoring and Secret Price Cuts

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  • Hitoshi Matsushima

    (Faculty of Economics, University of Tokyo)

Abstract

This paper investigates general two-player infinitely repeated games where the discount factor is less than but close to unity. We assume that monitoring is imperfect and private, and players' private signals are correlated through the unobservable macro shock. We show that a sequential equilibrium payoff vector approximates efficiency in a wide class of environments when the size of the set of private signals for each player is sufficiently large in comparison with the size of the set of possible macro shocks as well as the size of the set of actions for the opponent. We require almost no condition on the accuracy of players' monitoring technology. We argue that the use of review strategy works very well in the private monitoring case, although it does not work well in the public monitoring case. We apply our efficiency result to a model of price-setting duopoly a la Stigler (1964), where each firm's price choice is unobservable to its rival firm and the sales level for each firm is regarded as its private signal. Contrarily to Stigler's conjecture, the full cartel collusion can be self-enforcing even if firms cannot communicate and have the option of making secret price cuts.

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File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2002/2002cf154.pdf
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Bibliographic Info

Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-154.

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Length: 38 pages
Date of creation: Jun 2002
Date of revision:
Handle: RePEc:tky:fseres:2002cf154

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References

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  1. Radner, Roy, 1985. "Repeated Principal-Agent Games with Discounting," Econometrica, Econometric Society, vol. 53(5), pages 1173-98, September.
  2. Michihiro Kandori & Ichiro Obara, 2006. "Efficiency in Repeated Games Revisited: The Role of Private Strategies," Econometrica, Econometric Society, vol. 74(2), pages 499-519, 03.
  3. George Mailath & Stephen Morris, . ""Repeated Games with Almost-Public Monitoring''," CARESS Working Papres 99-09, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  4. Green, Edward J & Porter, Robert H, 1984. "Noncooperative Collusion under Imperfect Price Information," Econometrica, Econometric Society, vol. 52(1), pages 87-100, January.
  5. 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.
  6. 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.
  7. V. Bhaskar & Ichiro Obara, . "Belief-Based Equilibria in the Repeated Prisoners' Dilemma with Private Monitoring," Penn CARESS Working Papers d93eb6f40c65728f9e1a7b114, Penn Economics Department.
  8. Olivier Compte, 1998. "Communication in Repeated Games with Imperfect Private Monitoring," Econometrica, Econometric Society, vol. 66(3), pages 597-626, May.
  9. 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.
  10. Drew Fudenberg & David K. Levine & Eric Maskin, 1994. "The Folk Theorem with Imperfect Public Information," Levine's Working Paper Archive 394, David K. Levine.
  11. Hitoshi Matsushima, 1998. "Multimarket Contact, Imperfect Monitoring, and Implicit Collusion," CIRJE F-Series CIRJE-F-24, CIRJE, Faculty of Economics, University of Tokyo.
  12. Michihiro Kandori, 2001. "Introduction to Repeated Games with Private Monitoring," CIRJE F-Series CIRJE-F-114, CIRJE, Faculty of Economics, University of Tokyo.
  13. Aoyagi, Masaki, 2002. "Collusion in Dynamic Bertrand Oligopoly with Correlated Private Signals and Communication," Journal of Economic Theory, Elsevier, vol. 102(1), pages 229-248, January.
  14. Matsushima, Hitoshi, 1989. "Efficiency in repeated games with imperfect monitoring," Journal of Economic Theory, Elsevier, vol. 48(2), pages 428-442, August.
  15. Hitoshi Matsushima, 2000. "The Folk Theorem with Private Monitoring and Uniform Sustainability," CIRJE F-Series CIRJE-F-84, CIRJE, Faculty of Economics, University of Tokyo.
  16. Ichiro Obara, 2000. "Private Strategy and Efficiency: Repeated Partnership Games Revisited," Econometric Society World Congress 2000 Contributed Papers 1449, Econometric Society.
  17. Rotemberg, Julio J & Saloner, Garth, 1986. "A Supergame-Theoretic Model of Price Wars during Booms," American Economic Review, American Economic Association, vol. 76(3), pages 390-407, June.
  18. 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.
  19. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
  20. 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, 2003. "Repeated Games with Private Monitoring: Two Players," CIRJE F-Series CIRJE-F-242, CIRJE, Faculty of Economics, University of Tokyo.

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