IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpga/9605003.html
   My bibliography  Save this paper

On the Finiteness of Stable Sets

Author

Listed:
  • John Hillas

    (SUNY at Stony Brook)

  • Dries Vermeulen

    (University of Limburg)

  • Mathijs Jansen

    (University of Limburg)

Abstract

For two person games, stable sets in the sense of Kohlberg and Mertens and quasi-stable sets in the sense of Hillas are finite. In this paper we present an example to show that these sets are not necessarily finite in games with more than two players.

Suggested Citation

  • John Hillas & Dries Vermeulen & Mathijs Jansen, 1996. "On the Finiteness of Stable Sets," Game Theory and Information 9605003, University Library of Munich, Germany, revised 15 Jun 1996.
    • Handle: RePEc:wpa:wuwpga:9605003
    Note: Type of Document - AMS LaTeX; prepared on IBM PC ; to print on PostScript (or almost anything else if you can process the dvi file);
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/9605/9605003.ps.gz
    Download Restriction: no
    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/9605/9605003.pdf
    Download Restriction: no
    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/9605/9605003.tex
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jean-François Mertens, 1989. "Stable Equilibria---A Reformulation," Mathematics of Operations Research, INFORMS, vol. 14(4), pages 575-625, November.
    2. Jansen M. J. M. & Jurg A. P. & Borm P. E. M., 1994. "On Strictly Perfect Sets," Games and Economic Behavior, Elsevier, vol. 6(3), pages 400-415, May.
    3. MERTENS, Jean-François, 1991. "Stable equilibria - a reformulation. Part II. Discussion of the definition, and further results," LIDAM Reprints CORE 960, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    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. Belderbos, Rene & Carree, Martin & Lokshin, Boris, 2004. "Cooperative R&D and firm performance," Research Policy, Elsevier, vol. 33(10), pages 1477-1492, December.
    2. John Hillas & Elon Kohlberg, 1996. "Foundations of Strategic Equilibrium," Game Theory and Information 9606002, University Library of Munich, Germany, revised 18 Sep 1996.

    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. Bajoori, Elnaz & Flesch, János & Vermeulen, Dries, 2016. "Behavioral perfect equilibrium in Bayesian games," Games and Economic Behavior, Elsevier, vol. 98(C), pages 78-109.
    2. Demichelis, Stefano & Ritzberger, Klaus, 2003. "From evolutionary to strategic stability," Journal of Economic Theory, Elsevier, vol. 113(1), pages 51-75, November.
    3. GRIGIS DE STEFANO, Federico, 2014. "Strategic stability of equilibria: the missing paragraph," LIDAM Discussion Papers CORE 2014015, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Govindan, Srihari & Wilson, Robert B., 2008. "Axiomatic Theory of Equilibrium Selection in Signaling Games with Generic Payoffs," Research Papers 2000, Stanford University, Graduate School of Business.
    5. Srihari Govindan & Robert Wilson, 2012. "Axiomatic Equilibrium Selection for Generic Two‐Player Games," Econometrica, Econometric Society, vol. 80(4), pages 1639-1699, July.
    6. Balkenborg, Dieter & Vermeulen, Dries, 2014. "Universality of Nash components," Games and Economic Behavior, Elsevier, vol. 86(C), pages 67-76.
    7. Kleppe, John & Borm, Peter & Hendrickx, Ruud, 2012. "Fall back equilibrium," European Journal of Operational Research, Elsevier, vol. 223(2), pages 372-379.
    8. Meroni, Claudia & Pimienta, Carlos, 2017. "The structure of Nash equilibria in Poisson games," Journal of Economic Theory, Elsevier, vol. 169(C), pages 128-144.
    9. John Hillas & Mathijs Jansen & Jos Potters & Dries Vermeulen, 2001. "On the Relation Among Some Definitions of Strategic Stability," Mathematics of Operations Research, INFORMS, vol. 26(3), pages 611-635, August.
    10. Bajoori, Elnaz & Flesch, János & Vermeulen, Dries, 2013. "Perfect equilibrium in games with compact action spaces," Games and Economic Behavior, Elsevier, vol. 82(C), pages 490-502.
    11. Anesi, Vincent, 2010. "Noncooperative foundations of stable sets in voting games," Games and Economic Behavior, Elsevier, vol. 70(2), pages 488-493, November.
    12. Dieter Balkenborg & Josef Hofbauer & Christoph Kuzmics, 2015. "The refined best-response correspondence in normal form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 165-193, February.
    13. Srihari Govindan & Robert Wilson, 2008. "Metastable Equilibria," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 787-820, November.
    14. Govindan, Srihari & Wilson, Robert B., 2007. "Stable Outcomes of Generic Games in Extensive Form," Research Papers 1933r, Stanford University, Graduate School of Business.
    15. Vida, Péter & Honryo, Takakazu, 2021. "Strategic stability of equilibria in multi-sender signaling games," Games and Economic Behavior, Elsevier, vol. 127(C), pages 102-112.
    16. Stefano Demichelis & Klaus Ritzberger & Jeroen M. Swinkels, 2004. "The simple geometry of perfect information games," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(3), pages 315-338, June.
    17. DE SINOPOLI, Francesco, 1999. "Two examples of strategic equilibria in approval voting games," LIDAM Discussion Papers CORE 1999031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    18. Alós-Ferrer, Carlos, 2022. "The Trembling Chairman Paradox," Games and Economic Behavior, Elsevier, vol. 131(C), pages 51-56.
    19. Dieter Balkenborg & Stefano Demichelis & Dries Vermeulen, 2010. "Where strategic and evolutionary stability depart - a study of minimal diversity games," Discussion Papers 1001, University of Exeter, Department of Economics.
    20. Ohnishi, Kazuhiro, 2018. "Non-Altruistic Equilibria," MPRA Paper 88347, University Library of Munich, Germany.

    More about this item

    Keywords

    stable sets; Kohlberg and Mertens stability; quasi-stable sets;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

    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:wpa:wuwpga:9605003. 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: EconWPA (email available below). General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    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.