IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-04305157.html

On sustainable equilibria

Author

Listed:
  • Srihari Govindan

    (University of Rochester [USA])

  • Rida Laraki

    (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique, University of Liverpool, UM6P - Université Mohammed VI Polytechnique = Mohammed VI Polytechnic University [Ben Guerir])

  • Lucas Pahl

    (Universität Bonn = University of Bonn)

Abstract

Following the ideas laid out in Myerson (1996), Hofbauer (2003) defined a Nash equilibrium of a finite game as sustainable if it can be made the unique Nash equilibrium of a game obtained by deleting/adding a subset of the strategies that are inferior replies to it. This paper proves a result about sustainable equilibria and uses it to provide a refinement as well. Our result concerns the Hofbauer-Myerson conjecture about the relationship between the sustainability of an equilibrium and its index: for a generic class of games, an equilibrium is sustainable iff its index is +1. von Schemde and von Stengel (2008) proved this conjecture for bimatrix games; we show that the conjecture is true for all finite games. More precisely, we prove that an equilibrium is isolated and has index +1 if and only if it can be made unique in a larger game obtained by adding finitely many strategies that are inferior replies to that equilibrium. It follows in a straightforward way from our result that sustainable equilibria fail the Decomposition Axiom for games as formulated by Mertens (1989a). In order to rectify this problem we propose a refinement, called strongly sustainable equilibria, which is shown to exist for all regular games.

Suggested Citation

  • Srihari Govindan & Rida Laraki & Lucas Pahl, 2023. "On sustainable equilibria," Post-Print hal-04305157, HAL.
    • Handle: RePEc:hal:journl:hal-04305157
    DOI: 10.1016/j.jet.2023.105736
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    Other versions of this item:

    Citations

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


    Cited by:

    1. Lucas Pahl & Carlos Pimienta, 2024. "Robust Equilibria in Generic Extensive form Games," Papers 2412.18449, arXiv.org, revised Mar 2025.
    2. Ritzberger, Klaus & Weibull, Jörgen W. & Wikman, Peter, 2025. "Solid outcomes in finite games," Journal of Economic Theory, Elsevier, vol. 224(C).

    More about this item

    Keywords

    ;
    ;
    ;

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • 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:hal:journl:hal-04305157. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.