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Some Asymptotic Results in Discounted Repeated Games of One-Sided Incomplete Information

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  • Martin W. Cripps
  • Jonathan Thomas

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Abstract

The paper analyzes the Nash equilibria of two-person discounted repeated games with one-sided incomplete information and known own payo®s. If the informed player is arbitrarily patient relative to the uninformed player, then the characterization for the informed player's payoffs is essentially the same as that in the undiscounted case. This implies that even small amounts of incomplete information can lead to a discontinuous change in the equilibrium payoff set. For the case of equal discount factors, however, and under an assumption that strictly individually rational payoffs exist, a result akin to the Folk Theorem holds when a complete information game is perturbed by a small amount of incomplete information.

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File URL: http://www.econ.ed.ac.uk/papers/nashed.pdf
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Bibliographic Info

Paper provided by Edinburgh School of Economics, University of Edinburgh in its series ESE Discussion Papers with number 76.

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Length: 49
Date of creation: Mar 2004
Date of revision:
Handle: RePEc:edn:esedps:76

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Keywords: Reputation; Folk Theorem; repeated games; incomplete information.;

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References

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  1. Fudenberg, Drew & Maskin, Eric, 1991. "On the dispensability of public randomization in discounted repeated games," Journal of Economic Theory, Elsevier, vol. 53(2), pages 428-438, April.
  2. FORGES, Françoise, . "Repeated games of incomplete information: Non-zero sum," CORE Discussion Papers RP -1012, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. James Bergin, 1986. "A Characterization of Sequential Equilibrium Strategies in Infinitely Repeated Incomplete Information Games," Discussion Papers 686, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Cripps, Martin W. & Schmidt, Klaus M. & Thomas, Jonathan P., 1996. "Reputation in Perturbed Repeated Games," Journal of Economic Theory, Elsevier, vol. 69(2), pages 387-410, May.
  5. Cripps, Martin W. & Schmidt, Klaus M. & Thomas, Jonathan P., 1996. "Reputation in perturbed repeated games," Munich Reprints in Economics 20052, University of Munich, Department of Economics.
  6. E. Kalai & E. Lehrer, 2010. "Rational Learning Leads to Nash Equilibrium," Levine's Working Paper Archive 529, David K. Levine.
  7. Sorin, Sylvain, 1999. "Merging, Reputation, and Repeated Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 274-308, October.
  8. Shalev Jonathan, 1994. "Nonzero-Sum Two-Person Repeated Games with Incomplete Information and Known-Own Payoffs," Games and Economic Behavior, Elsevier, vol. 7(2), pages 246-259, September.
  9. Zamir, Shmuel, 1992. "Repeated games of incomplete information: Zero-sum," 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 5, pages 109-154 Elsevier.
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Cited by:
  1. Nicolas Jacquemet & Frédéric Koessler, 2013. "Using or Hiding Private Information? An Experimental Study of Zero-Sum Repeated Games with Incomplete Information," Post-Print halshs-00773412, HAL.
  2. Stefano, LOVO, 2007. "Belief-free equilibria in games with incomplete information," Les Cahiers de Recherche 884, HEC Paris.
  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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