IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v33y2005i4p479-490.html
   My bibliography  Save this article

An axiomatization of minimal curb sets

Author

Listed:
  • Mark Voorneveld
  • Willemien Kets
  • Henk Norde

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.)

Suggested Citation

  • Mark Voorneveld & Willemien Kets & Henk Norde, 2005. "An axiomatization of minimal curb sets," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(4), pages 479-490, November.
    • Handle: RePEc:spr:jogath:v:33:y:2005:i:4:p:479-490
    DOI: 10.1007/s00182-005-0208-6
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00182-005-0208-6
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00182-005-0208-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    4. Basu, Kaushik & Weibull, Jorgen W., 1991. "Strategy subsets closed under rational behavior," Economics Letters, Elsevier, vol. 36(2), pages 141-146, June.
    5. Chwe Michael Suk-Young, 1994. "Farsighted Coalitional Stability," Journal of Economic Theory, Elsevier, vol. 63(2), pages 299-325, August.
    6. Voorneveld, Mark, 2004. "Preparation," Games and Economic Behavior, Elsevier, vol. 48(2), pages 403-414, August.
    7. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Ehud Kalai & Dov Samet, 1982. "Persistent Equilibria in Strategic Games," Discussion Papers 515, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    13. 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.
    14. Voorneveld, Mark, 2005. "Persistent retracts and preparation," Games and Economic Behavior, Elsevier, vol. 51(1), pages 228-232, April.
    15. 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.
    16. Hurkens Sjaak, 1995. "Learning by Forgetful Players," Games and Economic Behavior, Elsevier, vol. 11(2), pages 304-329, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. Kets, W., 2008. "Networks and learning in game theory," Other publications TiSEM 7713fce1-3131-498c-8c6f-3, Tilburg University, School of Economics and Management.
    4. Kets, W. & Voorneveld, M., 2005. "Learning to be Prepared," Discussion Paper 2005-117, Tilburg University, Center for Economic Research.
    5. 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.
    6. 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.
    7. Paul Weithman, 2023. "Fixed points and well-ordered societies," Politics, Philosophy & Economics, , vol. 22(2), pages 197-212, May.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kets, W., 2008. "Networks and learning in game theory," Other publications TiSEM 7713fce1-3131-498c-8c6f-3, Tilburg University, School of Economics and Management.
    2. Voorneveld, Mark, 2004. "Preparation," Games and Economic Behavior, Elsevier, vol. 48(2), pages 403-414, August.
    3. Kets, Willemien & Voorneveld, Mark, 2005. "Learning to be prepared," SSE/EFI Working Paper Series in Economics and Finance 590, Stockholm School of Economics.
    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. Geir B. Asheim & Mark Voorneveld & Jörgen Weibull, 2009. "Epistemically stable strategy sets," Working Papers hal-00440098, HAL.
    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. Rene Saran & Roberto Serrano, 2012. "Regret Matching with Finite Memory," Dynamic Games and Applications, Springer, vol. 2(1), pages 160-175, March.
    8. Geir B. Asheim & Mark Voorneveld & Jörgen W. Weibull, 2016. "Epistemically Robust Strategy Subsets," Games, MDPI, vol. 7(4), pages 1-16, November.
    9. Balkenborg, Dieter & Hofbauer, Josef & Kuzmics, Christoph, 2016. "Refined best reply correspondence and dynamics," Center for Mathematical Economics Working Papers 451, Center for Mathematical Economics, Bielefeld University.
    10. Werner Güth, 2002. "On the Inconsistency of Equilibrium Refinement," Theory and Decision, Springer, vol. 53(4), pages 371-392, December.
    11. Voorneveld, Mark, 2002. "Preparation and toolkit learning," SSE/EFI Working Paper Series in Economics and Finance 485, Stockholm School of Economics.
    12. Christian Ewerhart, 2020. "Ordinal potentials in smooth games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 1069-1100, November.
    13. Weibull, Jorgen W., 1998. "Evolution, rationality and equilibrium in games," European Economic Review, Elsevier, vol. 42(3-5), pages 641-649, May.
    14. Peleg, Bezalel & Sudholter, Peter, 1997. "An Axiomatization of Nash Equilibria in Economic Situations," Games and Economic Behavior, Elsevier, vol. 18(2), pages 277-285, February.
    15. 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.
    16. Burkhard C. Schipper, 2022. "Strategic Teaching and Learning in Games," American Economic Journal: Microeconomics, American Economic Association, vol. 14(3), pages 321-352, August.
    17. Gonzalez, Stéphane & Lardon, Aymeric, 2021. "Axiomatic foundations of the core for games in effectiveness form," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 28-38.
    18. Stéphane Gonzalez & Aymeric Lardon, 2018. "Axiomatic Foundations of a Unifying Concept of the Core of Games in Effectiveness Form," GREDEG Working Papers 2018-15, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    19. Voorneveld, Mark, 2019. "An axiomatization of the Nash equilibrium concept," Games and Economic Behavior, Elsevier, vol. 117(C), pages 316-321.
    20. Stéphane Gonzalez & Aymeric Lardon, 2018. "Axiomatic Foundations of a Unifying Core," Working Papers 1817, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.

    More about this item

    Keywords

    Minimal curb set; Consistency; C72;
    All these keywords.

    JEL classification:

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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jogath:v:33:y:2005:i:4:p:479-490. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.