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On Finding Curb Sets in Extensive Games

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  • Vitaly Pruzhansky

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    (Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam)

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    Abstract

    We characterize strategy sets that are closed under rational behavior (curb) in extensive games of perfect information and finite horizon. It is shown that any such game possesses only one minimal curb set, which necessarily includes all its subgame perfect Nash equilibria. Applications of this result are twofold. First, it lessens computational burden while computing minimal curb sets. Second, it implies that the profile of subgame perfect equilibrium strategies is always stochastically stable in a certain class of games.

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    File URL: http://papers.tinbergen.nl/03098.pdf
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    Bibliographic Info

    Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 03-098/1.

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    Date of creation: 08 Dec 2003
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    Handle: RePEc:dgr:uvatin:20030098

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    Related research

    Keywords: rationalizability; stochastic stability;

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    1. Sergiu Hart, 1999. "Evolutionary Dynamics and Backward Induction," Game Theory and Information 9905002, EconWPA, revised 23 Mar 2000.
    2. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
    3. Basu, K. & Weibull, J., 1990. "Strategy Subsets Closed Under Rational Behavior," Papers 62, Princeton, Woodrow Wilson School - Discussion Paper.
    4. Martin J Osborne & Ariel Rubinstein, 2009. "A Course in Game Theory," Levine's Bibliography 814577000000000225, UCLA Department of Economics.
    5. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    6. Noldeke Georg & Samuelson Larry, 1993. "An Evolutionary Analysis of Backward and Forward Induction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 425-454, July.
    7. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
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    Cited by:
    1. Jacques Durieu & Hans Haller & Nicolas Quérou & Philippe Solal, 2007. "Ordinal Games," Post-Print ujm-00194794, HAL.
    2. Tercieux, O.R.C. & Voorneveld, M., 2005. "The Cutting Power of Preparation," Discussion Paper 2005-94, Tilburg University, Center for Economic Research.
    3. John Duggan & Michel Le Breton, 2014. "Choice-theoretic Solutions for Strategic Form Games," RCER Working Papers 580, University of Rochester - Center for Economic Research (RCER).

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