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An Axiomatization of Minimal Curb Sets

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  • Voorneveld, M.

    (Tilburg University, Center For Economic Research)

  • Kets, W.

    (Tilburg University, Center For Economic Research)

  • Norde, H.W.

    (Tilburg University, Center For Economic Research)

Abstract

Norde et al. [Games Econ. Behav. 12 (1996) 219] proved that none of the equilibrium concepts in the literature on equilibrium selection in finite strategic games satisfying existence is consistent. A transition to set-valued solution concepts overcomes the inconsistency problem: there is a multiplicity of consistent set-valued solution concepts that satisfy nonemptiness and recommend utility maximization in one-player games. The minimal curb sets of Basu and Weibull [Econ. Letters 36 (1991) 141] constitute one such solution concept; they are axiomatized in this article.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Voorneveld, M. & Kets, W. & Norde, H.W., 2005. "An Axiomatization of Minimal Curb Sets," Discussion Paper 2005-53, Tilburg University, Center for Economic Research.
    • Handle: RePEc:tiu:tiucen:69b8ae9b-dda3-475c-8f75-e817b661e2e2
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    1. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    2. Chwe Michael Suk-Young, 1994. "Farsighted Coalitional Stability," Journal of Economic Theory, Elsevier, vol. 63(2), pages 299-325, August.
    3. Voorneveld, Mark, 2004. "Preparation," Games and Economic Behavior, Elsevier, vol. 48(2), pages 403-414, August.
    4. Basu, Kaushik & Weibull, Jorgen W., 1991. "Strategy subsets closed under rational behavior," Economics Letters, Elsevier, vol. 36(2), pages 141-146, June.
    5. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    6. Martin Dufwenberg & Henk Norde & Hans Reijnierse & Stef Tijs, 2001. "The consistency principle for set-valued solutions and a new direction for normative game theory," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(1), pages 119-131, October.
    7. Peleg, Bezalel & Potters, Jos A M & Tijs, Stef H, 1996. "Minimality of Consistent Solutions for Strategic Games, in Particular for Potential Games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(1), pages 81-93, January.
    8. Norde, Henk & Potters, Jos & Reijnierse, Hans & Vermeulen, Dries, 1996. "Equilibrium Selection and Consistency," Games and Economic Behavior, Elsevier, vol. 12(2), pages 219-225, February.
    9. Ehud Kalai & Dov Samet, 1982. "Persistent Equilibria in Strategic Games," Discussion Papers 515, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    10. Patrone, F. & Pieri, G. & Tijs, S.H. & Torre, A., 1996. "On Consistent Solutions for Strategic Games," Other publications TiSEM 07b489e5-dff2-45d0-bd65-1, Tilburg University, School of Economics and Management.
    11. Peleg, Bezalel & Tijs, Stef, 1996. "The Consistency Principle for Games in Strategic Forms," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(1), pages 13-34.
    12. Patrone, F. & Pieri, G. & Tijs, S.H. & Torre, A., 1996. "On Consistent Solutions for Strategic Games," Research Memorandum 732, Tilburg University, School of Economics and Management.
    13. van Damme, Eric, 1998. "On the State of the Art in Game Theory: An Interview with Robert Aumann," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 181-210, July.
    14. Hurkens Sjaak, 1995. "Learning by Forgetful Players," Games and Economic Behavior, Elsevier, vol. 11(2), pages 304-329, November.
    15. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, April.
    16. Voorneveld, Mark, 2005. "Persistent retracts and preparation," Games and Economic Behavior, Elsevier, vol. 51(1), pages 228-232, April.
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    1. Tercieux, O.R.C. & Voorneveld, M., 2005. "The Cutting Power of Preparation," Other publications TiSEM 75173341-627f-4eb2-91f1-0, Tilburg University, School of Economics and Management.
    2. Kets, W., 2008. "Networks and learning in game theory," Other publications TiSEM 7713fce1-3131-498c-8c6f-3, Tilburg University, School of Economics and Management.
    3. Kets, W. & Voorneveld, M., 2005. "Learning to be Prepared," Discussion Paper 2005-117, Tilburg University, Center for Economic Research.
    4. Gilles Grandjean & Ana Mauleon & Vincent Vannetelbosch, 2017. "Strongly rational sets for normal-form games," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 35-46, April.
    5. Paul Weithman, 2023. "Fixed points and well-ordered societies," Politics, Philosophy & Economics, , vol. 22(2), pages 197-212, May.
    6. 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.
    7. 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.

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    More about this item

    Keywords

    Minimal curb set; Consistency;

    JEL classification:

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

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