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Comparison of information structures in stochastic games with imperfect public monitoring

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  • Daehyun Kim

    (UCLA)

Abstract

This paper studies the impact of an improvement of information structure upon the perfect public equilibrium payoff set in discounted stochastic games with imperfect public monitoring. We first suggest three partial orders on information structures in stochastic games. Although each of them reduces to the notion of garbling in repeated games (Kandori in Rev Econ Stud 59:581–593, 1992), we find that an improvement of information in terms of our two garbling notions does not imply an expansion of the equilibrium payoff set for some games. We also show that more informativeness in terms of our third notion of garbling is sufficient for the expansion, thereby extending the well-known monotonicity result in Kandori (1992) to stochastic games.

Suggested Citation

  • Daehyun Kim, 2019. "Comparison of information structures in stochastic games with imperfect public monitoring," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(1), pages 267-285, March.
    • Handle: RePEc:spr:jogath:v:48:y:2019:i:1:d:10.1007_s00182-018-0643-9
    DOI: 10.1007/s00182-018-0643-9
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    References listed on IDEAS

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    1. Fudenberg, Drew & Yamamoto, Yuichi, 2011. "The folk theorem for irreducible stochastic games with imperfect public monitoring," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1664-1683, July.
    2. Sugaya, Takuo & Wolitzky, Alexander, 2017. "Bounding equilibrium payoffs in repeated games with private monitoring," Theoretical Economics, Econometric Society, vol. 12(2), May.
    3. Hirshleifer, Jack, 1971. "The Private and Social Value of Information and the Reward to Inventive Activity," American Economic Review, American Economic Association, vol. 61(4), pages 561-574, September.
    4. Kamada, Yuichiro & Kominers, Scott Duke, 2010. "Information can wreck cooperation: A counterpoint to Kandori (1992)," Economics Letters, Elsevier, vol. 107(2), pages 112-114, May.
    5. Mailath George J. & Matthews Steven A. & Sekiguchi Tadashi, 2002. "Private Strategies in Finitely Repeated Games with Imperfect Public Monitoring," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 2(1), pages 1-23, June.
    6. Gossner, Olivier, 2000. "Comparison of Information Structures," Games and Economic Behavior, Elsevier, vol. 30(1), pages 44-63, January.
    7. Lehrer, Ehud & Rosenberg, Dinah & Shmaya, Eran, 2013. "Garbling of signals and outcome equivalence," Games and Economic Behavior, Elsevier, vol. 81(C), pages 179-191.
    8. Kloosterman, Andrew, 2015. "Public information in Markov games," Journal of Economic Theory, Elsevier, vol. 157(C), pages 28-48.
    9. Michihiro Kandori, 1992. "The Use of Information in Repeated Games with Imperfect Monitoring," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(3), pages 581-593.
    10. Johannes Hörner & Takuo Sugaya & Satoru Takahashi & Nicolas Vieille, 2011. "Recursive Methods in Discounted Stochastic Games: An Algorithm for δ→ 1 and a Folk Theorem," Econometrica, Econometric Society, vol. 79(4), pages 1277-1318, July.
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    Cited by:

    1. Daehyun Kim & Ichiro Obara, 2023. "On the Value of Information Structures in Stochastic Games," Papers 2308.09211, arXiv.org.

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    More about this item

    Keywords

    Stochastic game; Blackwell sufficiency; Information structure; Public monitoring; Perfect public equilibrium;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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