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Learning the state of nature in repeated games with incomplete information and signals

  • Renault, Jérôme
  • Tomala, Tristan

The motivation of this paper comes from repeated games with incomplete information and imperfect monitoring. It concerns the existence, for any payoff function, of a particular equilibrium (called completely revealing) allowing each player to learn the state of nature. We consider thus an interaction in which players, facing some incomplete information about the state of nature, exchange messages while imperfectly monitoring them. We then ask the question: can players learn the true state even under unilateral deviations? This problem is indeed closely related to Byzantine agreement problems from computer science. We define two different notions describing what a player can learn if at most one other player is faulty. We first link these notions with existence of completely revealing equilibria, then we characterize them for monitoring structures given by a graph. As a corollary we obtain existence of equilibria for a class of undiscounted repeated games.

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Paper provided by Paris Dauphine University in its series Economics Papers from University Paris Dauphine with number 123456789/6115.

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Date of creation: 2004
Date of revision:
Publication status: Published in Games and Economic Behavior, 2004, Vol. 47, no. 1. pp. 124-156.Length: 32 pages
Handle: RePEc:dau:papers:123456789/6115
Contact details of provider: Web page: http://www.dauphine.fr/en/welcome.html

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  1. GOSSNER, Olivier, 1997. "Secure protocols or how communication generates correlation," CORE Discussion Papers 1997092, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Ehud Lehrer & Sylvain Sorin, 1994. "One-Shot Public Mediated Talk," Discussion Papers 1108, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Gossner, Olivier & Vieille, Nicolas, 2001. "Repeated Communication Through the Mechanism And," Economics Papers from University Paris Dauphine 123456789/6031, Paris Dauphine University.
  4. JÊrÆme Renault & Tristan Tomala, 1998. "Repeated proximity games," International Journal of Game Theory, Springer, vol. 27(4), pages 539-559.
  5. Renault, Jérôme, 2001. "Learning Sets in State Dependent Signalling Game Forms: A Characterization," Economics Papers from University Paris Dauphine 123456789/6104, Paris Dauphine University.
  6. Robert J. Aumann & Sergiu Hart, 2002. "Long Cheap Talk," Discussion Paper Series dp284, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem, revised Nov 2002.
  7. 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.
  8. 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.
  9. Ehud Lehrer, 1988. "Internal Correlation in Repeated Games," Discussion Papers 800, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  10. Gossner, Olivier, 1998. "Secure Protocols or How Communication Generates Correlation," Economics Papers from University Paris Dauphine 123456789/6244, Paris Dauphine University.
  11. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, June.
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