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Evaluating information in zero-sum games with incomplete information on both sides

Author

Listed:
  • Bernard de Meyer

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Ehud Lehrer

    (TAU - School of Mathematical Sciences [Tel Aviv] - TAU - Raymond and Beverly Sackler Faculty of Exact Sciences [Tel Aviv] - TAU - Tel Aviv University)

  • Dinah Rosenberg

    (LAGA - Laboratoire Analyse, Géométrie et Applications - UP8 - Université Paris 8 Vincennes-Saint-Denis - UP13 - Université Paris 13 - Institut Galilée - CNRS - Centre National de la Recherche Scientifique)

Abstract

In a Bayesian game some players might receive a noisy signal regarding the specific game actually being played before it starts. We study zero-sum games where each player receives a partial information about his own type and no information about that of the other player and analyze the impact the signals have on the payoffs. It turns out that the functions that evaluate the value of information share two property. The first is Blackwell monotonicity, which means that each player gains from knowing more. The second is concavity on the space of conditional probabilities.

Suggested Citation

  • Bernard de Meyer & Ehud Lehrer & Dinah Rosenberg, 2009. "Evaluating information in zero-sum games with incomplete information on both sides," Post-Print halshs-00390625, HAL.
    • Handle: RePEc:hal:journl:halshs-00390625
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00390625
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    References listed on IDEAS

    as
    1. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, April.
    2. Lehrer, Ehud & Rosenberg, Dinah, 2006. "What restrictions do Bayesian games impose on the value of information?," Journal of Mathematical Economics, Elsevier, vol. 42(3), pages 343-357, June.
    3. Gilboa, Itzhak & Lehrer, Ehud, 1991. "The value of information - An axiomatic approach," Journal of Mathematical Economics, Elsevier, vol. 20(5), pages 443-459.
    4. Mertens, J.-F. & Zamir, S., 1980. "Minmax and maxmin of repeated games with incomplete information," LIDAM Reprints CORE 433, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Azrieli, Yaron & Lehrer, Ehud, 2008. "The value of a stochastic information structure," Games and Economic Behavior, Elsevier, vol. 63(2), pages 679-693, July.
    6. 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.
    7. Bernard de Meyer & Alexandre Marino, 2005. "Duality and optimal strategies in the finitely repeated zero-sum games with incomplete information on both sides," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00193996, HAL.
    8. Bruno Bassan & Olivier Gossner & Marco Scarsini & Shmuel Zamir, 2003. "Positive value of information in games," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(1), pages 17-31, December.
    9. Rida Laraki, 2002. "Repeated Games with Lack of Information on One Side: The Dual Differential Approach," Mathematics of Operations Research, INFORMS, vol. 27(2), pages 419-440, May.
    10. Neyman, Abraham, 1991. "The positive value of information," Games and Economic Behavior, Elsevier, vol. 3(3), pages 350-355, August.
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    Cited by:

    1. De Meyer, Bernard, 2010. "Price dynamics on a stock market with asymmetric information," Games and Economic Behavior, Elsevier, vol. 69(1), pages 42-71, May.
    2. Adam Kalai & Ehud Kalai, 2011. "Cooperation in Strategic Games Revisited," Discussion Papers 1512, Northwestern University, Center for Mathematical Studies in Economics and Management Science.

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    More about this item

    Keywords

    Value of information; Blackwell monotonicity; concavity; Valeur de l'information; monotonie à la Blackwell; concavité;
    All these keywords.

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