IDEAS home Printed from https://ideas.repec.org/p/hal/cesptp/halshs-00347438.html
   My bibliography  Save this paper

Stability Index of Interaction forms

Author

Listed:
  • Joseph Abdou

    () (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics)

Abstract

An interaction form is an abstract model of interaction based on a description of power distribution among agents over alternatives. A solution known as the settlement set is defined at any preference profile. Necessary and sufficient conditions for stability, that is the existence of settlements, are established. A Stability Index that plays a role similar to that of the Naka- mura Number is defined. It measures, loosely speaking, the complexity of those configurations that prevent a settlement. To any strategic game form one can associate an interaction form in such a way that given an equilibrium concept (e.g. Nash or strong Nash) and a preference profile, settlements of the interaction form are precisely the equilibrium outcomes of the resulting game. As a consequence we have necessary and sufficient conditions for the solvability of game forms. The paper provides a localization of the index in case of unstability.

Suggested Citation

  • Joseph Abdou, 2008. "Stability Index of Interaction forms," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00347438, HAL.
  • Handle: RePEc:hal:cesptp:halshs-00347438 Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00347438
    as

    Download full text from publisher

    File URL: https://halshs.archives-ouvertes.fr/halshs-00347438/document
    Download Restriction: no

    References listed on IDEAS

    as
    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, January.
    2. Richard Arena & Agnès Festré, 2002. "Connaissance et croyances en économie. L'exemple de la tradition autrichienne," Revue d'économie politique, Dalloz, vol. 112(5), pages 635-657.
    3. Arthur, W Brian, 1989. "Competing Technologies, Increasing Returns, and Lock-In by Historical Events," Economic Journal, Royal Economic Society, vol. 99(394), pages 116-131, March.
    4. Bernheim, B Douglas, 1994. "A Theory of Conformity," Journal of Political Economy, University of Chicago Press, vol. 102(5), pages 841-877, October.
    5. Hodgson, Geoffrey M, 1992. "Thorstein Veblen and Post-Darwinian Economics," Cambridge Journal of Economics, Oxford University Press, vol. 16(3), pages 285-301, September.
    6. Adam Gifford, 2007. "The knowledge problem, determinism, and The Sensory Order," The Review of Austrian Economics, Springer;Society for the Development of Austrian Economics, vol. 20(4), pages 269-291, December.
    7. Simon Gachter & Ernst Fehr, 2000. "Cooperation and Punishment in Public Goods Experiments," American Economic Review, American Economic Association, vol. 90(4), pages 980-994, September.
    8. Ragip Ege, 1992. "Émergence du marché concurrentiel et évolutionnisme chez Hayek," Revue Économique, Programme National Persée, vol. 43(6), pages 1007-1036.
    9. Ulrich Witt, 2006. "Evolutionary Economics," Papers on Economics and Evolution 2006-05, Philipps University Marburg, Department of Geography.
    10. Jeffery Carpenter & Samuel Bowles & Herbert Gintis, 2006. "Mutual Monitoring in Teams: Theory and Experimental Evidence on the Importance of Reciprocity," Middlebury College Working Paper Series 0608, Middlebury College, Department of Economics.
    11. Sethi, Rajiv & Somanathan, E, 1996. "The Evolution of Social Norms in Common Property Resource Use," American Economic Review, American Economic Association, vol. 86(4), pages 766-788, September.
    12. Leonid Hurwicz, 1994. "Economic design, adjustment processes, mechanisms, and institutions," Review of Economic Design, Springer;Society for Economic Design, vol. 1(1), pages 1-14, December.
    13. Daniel Kahneman, 2003. "Maps of Bounded Rationality: Psychology for Behavioral Economics," American Economic Review, American Economic Association, vol. 93(5), pages 1449-1475, December.
    14. Birner Jack, 1995. "The surprising place of cognitive psychology in the work of F.A. Hayek," Research Memorandum 019, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    15. Pierre Garrouste, 1999. "Le problème de la cohérence de l'évolutionnisme hayékien," Post-Print halshs-00274290, HAL.
    16. Garrouste, Pierre, 1994. "Menger and Hayek on Institutions: Continuity and Discontinuity," Journal of the History of Economic Thought, Cambridge University Press, vol. 16(02), pages 270-291, September.
    17. Luciano Andreozzi, 2005. "Hayek Reads the Literature on the Emergence of Norms," Constitutional Political Economy, Springer, vol. 16(3), pages 227-247, September.
    18. Hodgson, Geoffrey M., 1991. "Hayek's Theory of Cultural Evolution: An Evaluation in the Light of Vanberg's Critique," Economics and Philosophy, Cambridge University Press, vol. 7(01), pages 67-82, April.
    Full references (including those not matched with items on IDEAS)

    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:cesptp:halshs-00347438. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.