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Multiplayer belief revision

Author

Listed:
  • Antoine Billot

    (LEM - Laboratoire d'Économie Moderne - UP2 - Université Panthéon-Assas, PJSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Jean-Christophe Vergnaud

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

  • Bernard Walliser

    (PJSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

One main topic of the epistemic program of game theory deals with the value of information. To study this question in a broad context, one needs to adapt some of the tools used in multiplayer epistemic logic. A hierarchical belief structure is introduced both in a syntactical and semantical framework. In the same framework, a generalized notion of message is characterized by its content and its status. For a given message, a multiplayer belief revision rule that transforms any initial belief structure into a final belief one is designed. A representation theorem relates syntactical axioms to the belief revision rule.

Suggested Citation

  • Antoine Billot & Jean-Christophe Vergnaud & Bernard Walliser, 2008. "Multiplayer belief revision," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00344461, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00344461
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00344461
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    References listed on IDEAS

    as
    1. Giacomo Bonanno, 2004. "A simple modal logic for belief revision," Working Papers 164, University of California, Davis, Department of Economics.
    2. Robert J. Aumann, 1999. "Interactive epistemology II: Probability," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 301-314.
    3. 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.
    4. Neyman, Abraham, 1991. "The positive value of information," Games and Economic Behavior, Elsevier, vol. 3(3), pages 350-355, August.
    5. Giacomo Bonanno, 2004. "A simple modal logic for belief revision," Working Papers 45, University of California, Davis, Department of Economics.
    6. Board, Oliver, 2004. "Dynamic interactive epistemology," Games and Economic Behavior, Elsevier, vol. 49(1), pages 49-80, October.
    7. Gossner, Olivier, 2000. "Comparison of Information Structures," Games and Economic Behavior, Elsevier, vol. 30(1), pages 44-63, January.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    epistemic logic; Belief revision; message; epistemic logic.; Révision des croyances; logique épistémique.;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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