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On Finding Curb Sets in Extensive Games

Author

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  • Vitaly Pruzhansky

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

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.

Suggested Citation

  • Vitaly Pruzhansky, 2003. "On Finding Curb Sets in Extensive Games," Tinbergen Institute Discussion Papers 03-098/1, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20030098
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    References listed on IDEAS

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    Cited by:

    1. Jacques Durieu & Hans Haller & Nicolas Querou & Philippe Solal, 2008. "Ordinal Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 177-194.
    2. Milchtaich, Igal, 2019. "Polyequilibrium," Games and Economic Behavior, Elsevier, vol. 113(C), pages 339-355.
    3. P. Jean-Jacques Herings & Andrey Meshalkin & Arkadi Predtetchinski, 2020. "Optimality, Equilibrium, and Curb Sets in Decision Problems Without Commitment," Dynamic Games and Applications, Springer, vol. 10(2), pages 478-492, June.
    4. Olivier Tercieux & Mark Voorneveld, 2010. "The cutting power of preparation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(1), pages 85-101, February.
    5. 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).
    6. Igal Milchtaich, 2015. "Polyequilibrium," Working Papers 2015-06, Bar-Ilan University, Department of Economics.

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    More about this item

    Keywords

    rationalizability; stochastic stability;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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