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Communication equilibrium payoffs in repeated games with imperfect monitoring

  • Renault, Jérôme
  • Tomala, Tristan

We characterize the set of communication equilibrium payoffs of any undiscounted repeated matrix-game with imperfect monitoring and complete information. For two-player games, a characterization is provided by Mertens, Sorin, and Zamir (Repeated games, Part A (1994) CORE DP 9420), mainly using Lehrer's (Math. Operations Res. (1992) 175) result for correlated equilibria. The main result of this paper is to extend this characterization to the n-player case. The proof of the characterization relies on an analogy with an auxiliary 2-player repeated game with incomplete information and imperfect monitoring. We use Kohlberg's (Int. J. Game Theory (1975) 7) result to construct explicitly a canonical communication device for each communication equilibrium payoff.

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Paper provided by Paris Dauphine University in its series Economics Papers from University Paris Dauphine with number 123456789/6103.

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Date of creation: 2004
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Publication status: Published in Games and Economic Behavior, 2004, Vol. 49, no. 2. pp. 313-344.Length: 31 pages
Handle: RePEc:dau:papers:123456789/6103
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  1. Renault, J. & Tomala, T., 1997. "Repeated Proximity Games," Papiers d'Economie Mathématique et Applications 97.14, Université Panthéon-Sorbonne (Paris 1).
  2. Sorin, Sylvain, 1992. "Repeated games with complete information," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 4, pages 71-107 Elsevier.
  3. Jérôme Renault, 2001. "3-player repeated games with lack of information on one side," International Journal of Game Theory, Springer, vol. 30(2), pages 221-245.
  4. Myerson, Roger B., 1982. "Optimal coordination mechanisms in generalized principal-agent problems," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 67-81, June.
  5. Forges, F., 1984. "An approach to communication equilibria," CORE Discussion Papers 1984035, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Lehrer, E, 1989. "Lower Equilibrium Payoffs in Two-Player Repeated Games with Non-observable Actions," International Journal of Game Theory, Springer, vol. 18(1), pages 57-89.
  7. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, June.
  8. Lehrer, E, 1990. "Nash Equilibria of n-Player Repeated Games with Semi-standard Information," International Journal of Game Theory, Springer, vol. 19(2), pages 191-217.
  9. Tomala, Tristan, 1999. "Nash Equilibria of Repeated Games with Observable Payoff Vectors," Games and Economic Behavior, Elsevier, vol. 28(2), pages 310-324, August.
  10. Renault, Jérôme, 2000. "On Two-Player Repeated Games with Lack of Information on One Side and State-Independent Signalling," Economics Papers from University Paris Dauphine 123456789/6109, Paris Dauphine University.
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