IDEAS home Printed from https://ideas.repec.org/p/hal/pseptp/halshs-00633589.html
   My bibliography  Save this paper

Stability and Index of the Meet Game on a Lattice

Author

Listed:
  • Joseph M. Abdou

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

We study the stability and the stability index of the meet game form defined on a meet semilattice. Given any active coalition structure, we show that the stability index relative to the equilibrium, to the beta core and to the exact core is a function of the Nakamura number, the depth of the semilattice and its gap function.

Suggested Citation

  • Joseph M. Abdou, 2012. "Stability and Index of the Meet Game on a Lattice," PSE-Ecole d'économie de Paris (Postprint) halshs-00633589, HAL.
    • Handle: RePEc:hal:pseptp:halshs-00633589
    DOI: 10.1007/s00182-012-0339-5
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00633589
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-00633589/document
    Download Restriction: no
    File URL: https://libkey.io/10.1007/s00182-012-0339-5?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
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June.
    2. Peleg,Bezalel, 2008. "Game Theoretic Analysis of Voting in Committees," Cambridge Books, Cambridge University Press, number 9780521074650, October.
    3. Abdou, Joseph, 2010. "A stability index for local effectivity functions," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 306-313, May.
    4. Abdou, Joseph & Keiding, Hans, 2003. "On necessary and sufficient conditions for solvability of game forms," Mathematical Social Sciences, Elsevier, vol. 46(3), pages 243-260, December.
    5. repec:dau:papers:123456789/13220 is not listed on IDEAS
    6. Joseph Abdou, 2012. "The structure of unstable power mechanisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(2), pages 389-415, June.
    7. Abdou, J., 2000. "Exact stability and its applications to strong solvability," Mathematical Social Sciences, Elsevier, vol. 39(3), pages 263-275, May.
    Full references (including those not matched with items on IDEAS)

    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. repec:hal:wpaper:halshs-00633589 is not listed on IDEAS
    2. Joseph M. Abdou, 2009. "The Structure of Unstable Power Systems," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00389181, HAL.
    3. Joseph M. Abdou, 2008. "Stability Index of Interaction forms," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00347438, HAL.
    4. Abdou, Joseph, 2010. "A stability index for local effectivity functions," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 306-313, May.
    5. Bezalel Peleg & Ariel Procaccia, 2010. "Implementation by mediated equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 191-207, March.
    6. Murat R. Sertel & M. Remzi Sanver, 2004. "Strong equilibrium outcomes of voting games ¶are the generalized Condorcet winners," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(2), pages 331-347, April.
    7. Bezalel Peleg & Hans Peters, 2010. "Consistent voting systems with a continuum of voters," Studies in Choice and Welfare, in: Strategic Social Choice, chapter 0, pages 123-145, Springer.
    8. Abdou, Joseph & Keiding, Hans, 2009. "Interaction sheaves on continuous domains," Journal of Mathematical Economics, Elsevier, vol. 45(11), pages 708-719, December.
    9. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare,in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 5, pages 237-288 Elsevier.
    10. Joseph Abdou, 2012. "The structure of unstable power mechanisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(2), pages 389-415, June.
    11. Stefano Vannucci, 2004. "On Game Formats and Chu Spaces," Department of Economics University of Siena 417, Department of Economics, University of Siena.
    12. Stefano Vannucci, 2007. "Game Formats As Chu Spaces," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(01), pages 119-138.
    13. 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.
    14. Agnieszka Rusinowska, 2013. "Bezalel Peleg and Hans Peters: Strategic Social Choice. Stable Representations of Constitutions, Studies in choice and welfare, Springer, 2010, 154 pp," Post-Print hal-00666816, HAL.
    15. Salvador Barberà, 2010. "Strategy-proof social choice," UFAE and IAE Working Papers 828.10, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    16. Eyal Winter & Bezalel Peleg, 2002. "original papers : Constitutional implementation," Review of Economic Design, Springer;Society for Economic Design, vol. 7(2), pages 187-204.
    17. Abdou, Joseph & Keiding, Hans, 2003. "On necessary and sufficient conditions for solvability of game forms," Mathematical Social Sciences, Elsevier, vol. 46(3), pages 243-260, December.
    18. Abdou, J., 1998. "Tight and Effectively Rectangular Game Forms: A Nash Solvable Class," Games and Economic Behavior, Elsevier, vol. 23(1), pages 1-11, April.
    19. 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.
    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.
    21. Hans Keiding & Bezalel Peleg, 2006. "Binary effectivity rules," Review of Economic Design, Springer;Society for Economic Design, vol. 10(3), pages 167-181, December.

    More about this item

    Keywords

    Effectivity Function; Lattice; Stability Index; Equilibrium; Nakamura Number;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

    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:pseptp:halshs-00633589. 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: Caroline Bauer (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.