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Ability and Knowledge

Author

Listed:
  • Olivier Gossner

    (PSE - 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

In games with incomplete information, more information to a player implies a broader strategy set for this player in the normal form game, hence more knowledge implies more ability. We prove that, conversely, given two normal form games G and G′ such that players in a subset J of the set of players possess more strategies in G′ than in G, there exist two games with incomplete information with normal forms G and G′ such that players in J are more informed in the second than in the first. More ability can then be rationalized by more knowledge, and our result thus establishes the formal equivalence between ability and knowledge.

Suggested Citation

  • Olivier Gossner, 2010. "Ability and Knowledge," Post-Print halshs-00754449, HAL.
    • Handle: RePEc:hal:journl:halshs-00754449
    DOI: 10.1016/j.geb.2009.10.011
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    References listed on IDEAS

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    1. Vermeulen, Dries & Jansen, Mathijs, 1998. "The reduced form of a game," European Journal of Operational Research, Elsevier, vol. 106(1), pages 204-211, April.
    2. Bade, Sophie & Haeringer, Guillaume & Renou, Ludovic, 2007. "More strategies, more Nash equilibria," Journal of Economic Theory, Elsevier, vol. 135(1), pages 551-557, July.
    3. Jean-François Mertens, 2004. "Ordinality in non cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(3), pages 387-430, June.
    4. 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.
    5. Ehud Lehrer & Dinah Rosenberg, 2003. "Information and Its Value in Zero-Sum Repeated Games," Game Theory and Information 0312003, University Library of Munich, Germany.
    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. Gossner, Olivier, 2000. "Comparison of Information Structures," Games and Economic Behavior, Elsevier, vol. 30(1), pages 44-63, January.
    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. Neyman, Abraham, 1991. "The positive value of information," Games and Economic Behavior, Elsevier, vol. 3(3), pages 350-355, August.
    10. Kamien, Morton I. & Tauman, Yair & Zamir, Shmuel, 1990. "On the value of information in a strategic conflict," Games and Economic Behavior, Elsevier, vol. 2(2), pages 129-153, June.
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    Cited by:

    1. Mark Whitmeyer, 2020. "In Simple Communication Games, When Does Ex Ante Fact-Finding Benefit the Receiver?," Papers 2001.09387, arXiv.org.
    2. Bade, Sophie & Haeringer, Guillaume & Renou, Ludovic, 2007. "More strategies, more Nash equilibria," Journal of Economic Theory, Elsevier, vol. 135(1), pages 551-557, July.
    3. Bergemann, Dirk & Morris, Stephen, 2016. "Bayes correlated equilibrium and the comparison of information structures in games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    4. 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.
    5. Cédric Wanko, 2018. "A Unique and Stable $$\hbox {Se}{\mathcal {C}}\hbox {ure}$$ Se C ure Reversion Protocol Improving Efficiency: A Computational Bayesian Approach for Empirical Analysis," Computational Economics, Springer;Society for Computational Economics, vol. 52(1), pages 1-23, June.
    6. Bernard De Meyer & Ehud Lehrer & Dinah Rosenberg, 2010. "Evaluating Information in Zero-Sum Games with Incomplete Information on Both Sides," Mathematics of Operations Research, INFORMS, vol. 35(4), pages 851-863, November.

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