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

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  • Renault, Jerome
  • Tomala, Tristan

Abstract

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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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 47 (2004)
Issue (Month): 1 (April)
Pages: 124-156

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Handle: RePEc:eee:gamebe:v:47:y:2004:i:1:p:124-156

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Web page: http://www.elsevier.com/locate/inca/622836

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References

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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. Lehrer, Ehud & Sorin, Sylvain, 1997. "One-Shot Public Mediated Talk," Games and Economic Behavior, Elsevier, vol. 20(2), pages 131-148, August.
  3. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476.
  4. SORIN, Sylvain, 1988. "Repeated games with complete information," CORE Discussion Papers 1988022, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Lehrer, Ehud, 1991. "Internal Correlation in Repeated Games," International Journal of Game Theory, Springer, vol. 19(4), pages 431-56.
  6. Gossner, Olivier, 1998. "Secure Protocols or How Communication Generates Correlation," Economics Papers from University Paris Dauphine 123456789/6244, Paris Dauphine University.
  7. JÊrÆme Renault & Tristan Tomala, 1998. "Repeated proximity games," International Journal of Game Theory, Springer, vol. 27(4), pages 539-559.
  8. Gossner, Olivier & Vieille, Nicolas, 2001. "Repeated Communication Through the Mechanism And," Economics Papers from University Paris Dauphine 123456789/6031, Paris Dauphine University.
  9. Renault, Jérôme, 2001. "Learning Sets in State Dependent Signalling Game Forms: A Characterization," Economics Papers from University Paris Dauphine 123456789/6104, Paris Dauphine University.
  10. 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.
  11. Robert J. Aumann & Sergiu Hart, 2003. "Long Cheap Talk," Econometrica, Econometric Society, vol. 71(6), pages 1619-1660, November.
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Citations

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Cited by:
  1. Laclau, Marie, 2012. "A folk theorem for repeated games played on a network," Games and Economic Behavior, Elsevier, vol. 76(2), pages 711-737.
  2. Fudenberg, Drew & Yamamoto, Yuichi, 2011. "Learning from private information in noisy repeated games," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1733-1769, September.
  3. Lovo, Stefano & Tomala, Tristan & Hörner, Johannes, 2009. "Belief-free equilibria in games with incomplete information: characterization and existence," Les Cahiers de Recherche 921, HEC Paris.

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