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Epistemic conditions for rationalizability

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  • Zambrano, Eduardo

Abstract

In this paper I present conditions, not involving common knowledge of rationality, that lead to (correlated) rationalizability. The basic observation is that, if the actual world belongs to a set of states where the set Z of action profiles is played, everyone is rational and it is mutual knowledge that the action profiles played are in Z, then the actions played at the actual world are rationalizable actions. Alternatively, if at the actual world the support of the conjecture of player i is Di, there is mutual knowledge of: (i) the game being played, (ii) that the players are rational, and (iii) that for every i the support of the conjecture of player i is contained in Di, then every strategy in the support of the conjectures is rationalizable. The results do not require common knowledge of anything and are valid for games with any number of players.

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  • Zambrano, Eduardo, 2008. "Epistemic conditions for rationalizability," Games and Economic Behavior, Elsevier, vol. 63(1), pages 395-405, May.
    • Handle: RePEc:eee:gamebe:v:63:y:2008:i:1:p:395-405
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    Cited by:

    1. Tsakas, E., 2012. "Pairwise mutual knowledge and correlated rationalizability," Research Memorandum 031, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    2. Geir B. Asheim & Mark Voorneveld & Jörgen W. Weibull, 2016. "Epistemically Robust Strategy Subsets," Games, MDPI, vol. 7(4), pages 1-16, November.
    3. Giacomo Rubbini, 2023. "Mechanism Design without Rational Expectations," Papers 2305.07472, arXiv.org, revised Nov 2023.
    4. Geir B. , Asheim & Voorneveld, Max & W. Weibull, Jörgen, 2009. "Epistemically Stable Strategy Sets," Memorandum 01/2010, Oslo University, Department of Economics.
    5. Tsakas, Elias, 2013. "Pairwise epistemic conditions for correlated rationalizability," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 379-384.

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