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Ability and knowledge

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  • Gossner, Olivier

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

  • Gossner, Olivier, 2010. "Ability and knowledge," Games and Economic Behavior, Elsevier, vol. 69(1), pages 95-106, May.
    • Handle: RePEc:eee:gamebe:v:69:y:2010:i:1:p:95-106
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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.
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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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