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

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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 payoffs. 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.

Suggested Citation

  • Martin W. Cripps & Jonathan Thomas, 2001. "Some Asymptotic Results in Discounted Repeated Games of One-Sided Incomplete Information," Edinburgh School of Economics Discussion Paper Series 76, Edinburgh School of Economics, University of Edinburgh.
    • Handle: RePEc:edn:esedps:76
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    1. repec:dau:papers:123456789/184 is not listed on IDEAS
    2. Forges, Francoise, 1992. "Repeated games of incomplete information: Non-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 6, pages 155-177, Elsevier.
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    10. Sorin, Sylvain, 1999. "Merging, Reputation, and Repeated Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 274-308, October.
    11. Ehud Lehrer & Leeat Yariv, 1999. "Repeated Games with Incomplete Information on One Side: The Case of Different Discount Factors," Mathematics of Operations Research, INFORMS, vol. 24(1), pages 204-218, February.
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    Cited by:

    1. Johannes Hörner & Stefano Lovo, 2009. "Belief-Free Equilibria in Games With Incomplete Information," Econometrica, Econometric Society, vol. 77(2), pages 453-487, March.
    2. Jacquemet, Nicolas & Koessler, Frédéric, 2013. "Using or hiding private information? An experimental study of zero-sum repeated games with incomplete information," Games and Economic Behavior, Elsevier, vol. 78(C), pages 103-120.
    3. Hörner, Johannes & Lovo, Stefano & Tomala, Tristan, 2011. "Belief-free equilibria in games with incomplete information: Characterization and existence," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1770-1795, September.

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    More about this item

    Keywords

    reputation; Folk theorem; repeated games; incomplete information;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • L14 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Transactional Relationships; Contracts and Reputation

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