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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," Post-Print hal-00586037, HAL.
    • Handle: RePEc:hal:journl:hal-00586037
    DOI: 10.1287/moor.1100.0467
    as

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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Fabien Gensbittel & Marcin Peski & Jérôme Renault, 2019. "The Large Space Of Information Structures," Working Papers hal-02075905, HAL.

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