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Epistemic conditions for rationalizability

  • Zambrano, Eduardo
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    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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    File URL: http://www.sciencedirect.com/science/article/B6WFW-4R0KT53-2/1/03e2a27c57ab637505e15d1cd82747a5
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    Article provided by Elsevier in its journal Games and Economic Behavior.

    Volume (Year): 63 (2008)
    Issue (Month): 1 (May)
    Pages: 395-405

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    Handle: RePEc:eee:gamebe:v:63:y:2008:i:1:p:395-405
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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    1. Giacomo Bonanno & Pierpaolo Battigalli, 2003. "Recent Results On Belief, Knowledge And The Epistemic Foundations Of Game Theory," Working Papers 9814, University of California, Davis, Department of Economics.
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    8. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, vol. 55(6), pages 1391-1402, November.
    9. Ronald Fagin & Joseph Y. Halpern & Yoram Moses & Moshe Y. Vardi, 2003. "Reasoning About Knowledge," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262562006, June.
    10. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, June.
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    13. Adam Brandenburger, 1992. "Knowledge and Equilibrium in Games," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 83-101, Fall.
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