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Admissibility in Games

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  • Adam Brandenburger
  • Amanda Friedenberg
  • H. Jerome Keisler
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    Abstract

    Suppose that each player in a game is rational, each player thinks the other players are rational, and so on. Also, suppose that rationality is taken to incorporate an admissibility requirement-that is, the avoidance of weakly dominated strategies. Which strategies can be played? We provide an epistemic framework in which to address this question. Specifically, we formulate conditions of rationality and mth-order assumption of rationality (RmAR) and rationality and common assumption of rationality (RCAR). We show that (i) RCAR is characterized by a solution concept we call a "self-admissible set"; (ii) in a "complete" type structure, RmAR is characterized by the set of strategies that survive m+1 rounds of elimination of inadmissible strategies; (iii) under certain conditions, RCAR is impossible in a complete structure. Copyright The Econometric Society 2008.

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    File URL: http://hdl.handle.net/10.1111/j.0012-9682.2008.00835.x
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    Bibliographic Info

    Article provided by Econometric Society in its journal Econometrica.

    Volume (Year): 76 (2008)
    Issue (Month): 2 (03)
    Pages: 307-352

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    Handle: RePEc:ecm:emetrp:v:76:y:2008:i:2:p:307-352

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    Cited by:
    1. Robin P. Cubitt & Robert Sugden, 2010. "The reasoning-based expected utility procedure," Working Paper series, University of East Anglia, Centre for Behavioural and Experimental Social Science (CBESS) 09-04, School of Economics, University of East Anglia, Norwich, UK..
    2. Lucia Buenrostro & Amrita Dhillon & Peter Vida, 2013. "Scoring rule voting games and dominance solvability," Social Choice and Welfare, Springer, vol. 40(2), pages 329-352, February.
    3. Paulo Barelli & Spyros Galanis, 2011. "Admissibility and Event-Rationality," RCER Working Papers 568, University of Rochester - Center for Economic Research (RCER).
    4. Lee, Byung Soo, 2013. "Conditional Beliefs and Higher-Order Preferences," MPRA Paper 48551, University Library of Munich, Germany.
    5. Halpern, Joseph Y., 2010. "Lexicographic probability, conditional probability, and nonstandard probability," Games and Economic Behavior, Elsevier, vol. 68(1), pages 155-179, January.
    6. Liu, Qingmin, 2009. "On redundant types and Bayesian formulation of incomplete information," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2115-2145, September.
    7. Christian W. Bach & Conrad Heilmann, 2009. "Agent connectedness and backward induction," LSE Research Online Documents on Economics 27000, London School of Economics and Political Science, LSE Library.
    8. Brandenburger, Adam & Friedenberg, Amanda, 2010. "Self-admissible sets," Journal of Economic Theory, Elsevier, vol. 145(2), pages 785-811, March.
    9. Friedenberg, Amanda, 2010. "When do type structures contain all hierarchies of beliefs?," Games and Economic Behavior, Elsevier, vol. 68(1), pages 108-129, January.
    10. Jackson, Matthew O. & Tan, Xu, 2013. "Deliberation, disclosure of information, and voting," Journal of Economic Theory, Elsevier, vol. 148(1), pages 2-30.
    11. Perea, Andrés, 2011. "An algorithm for proper rationalizability," Games and Economic Behavior, Elsevier, vol. 72(2), pages 510-525, June.
    12. Keisler, H. Jerome & Lee, Byung Soo, 2011. "Common assumption of rationality," MPRA Paper 34441, University Library of Munich, Germany.
    13. Kartik, Navin & Tercieux, Olivier & Holden, Richard, 2014. "Simple mechanisms and preferences for honesty," Games and Economic Behavior, Elsevier, vol. 83(C), pages 284-290.
    14. Lo, Kin Chung, 2011. "Possibility and permissibility," Mathematical Social Sciences, Elsevier, vol. 62(2), pages 109-113, September.
    15. Salonen, Hannu, 2009. "Common theories," Mathematical Social Sciences, Elsevier, vol. 58(3), pages 279-289, November.
    16. Halpern, Joseph Y. & Pass, Rafael, 2012. "Iterated regret minimization: A new solution concept," Games and Economic Behavior, Elsevier, vol. 74(1), pages 184-207.

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