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Communication equilibrium payoffs in repeated games with imperfect monitoring

  • Renault, Jerome
  • 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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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 49 (2004)
Issue (Month): 2 (November)
Pages: 313-344

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Handle: RePEc:eee:gamebe:v:49:y:2004:i:2:p:313-344
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, June.
  2. Forges, F., 1984. "An approach to communication equilibria," CORE Discussion Papers 1984035, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. SORIN, Sylvain, 1988. "Repeated games with complete information," CORE Discussion Papers 1988022, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  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. 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.
  6. 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.
  7. Renault, Jérôme, 2001. "3-player repeated games with lack of information on one side," Economics Papers from University Paris Dauphine 123456789/6538, Paris Dauphine University.
  8. Tomala, Tristan, 1999. "Nash Equilibria of Repeated Games with Observable Payoff Vectors," Games and Economic Behavior, Elsevier, vol. 28(2), pages 310-324, August.
  9. 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.
  10. JÊrÆme Renault & Tristan Tomala, 1998. "Repeated proximity games," International Journal of Game Theory, Springer, vol. 27(4), pages 539-559.
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