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Evaluating Information in Zero-Sum Games with Incomplete Information on Both Sides

Author

Listed:
  • Dinah Rosenberg

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

  • 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)

Abstract

We study zero-sum games with incomplete information and analyze the impact that the information players receive has on the payoffs. It turns out that the functions that measure the value of information share two properties. The first is Blackwell monotonicity, which means that each player gains from knowing more. The second is concavity on the space of conditional probabilities. We prove that any function satisfying these two properties is the value function of a zero-sum game.

Suggested Citation

  • Dinah Rosenberg & Bernard de Meyer & Ehud Lehrer, 2010. "Evaluating Information in Zero-Sum Games with Incomplete Information on Both Sides," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00586037, HAL.
    • Handle: RePEc:hal:cesptp:hal-00586037
    DOI: 10.1287/moor.1100.0467
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    Citations

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    Cited by:

    1. Adam Kalai & Ehud Kalai, 2011. "Cooperation in Strategic Games Revisited," Discussion Papers 1512, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Mark Whitmeyer, 2020. "In Simple Communication Games, When Does Ex Ante Fact-Finding Benefit the Receiver?," Papers 2001.09387, arXiv.org.
    3. Yanling Chang & Alan Erera & Chelsea White, 2015. "Value of information for a leader–follower partially observed Markov game," Annals of Operations Research, Springer, vol. 235(1), pages 129-153, December.
    4. Fabien Gensbittel & Marcin Peski & Jérôme Renault, 2019. "The Large Space Of Information Structures," Working Papers hal-02075905, HAL.
    5. 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.
    6. Fabien Gensbittel, 2015. "Extensions of the Cav( u ) Theorem for Repeated Games with Incomplete Information on One Side," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 80-104, February.

    More about this item

    Keywords

    value-of-information function; zero-sum game; game with incomplete information; Blackwell monotonicity;
    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
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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