IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Characterizations of the Existence of Nash Equilibria with Non-convex Strategy Sets

  • Rabia Nessah

    ()

    (IESEG School of Management (LEM-CNRS))

  • Kristiaan Kerstens

    ()

    (CNRS-LEM (UMR 8179), IESEG School of Management)

A sufficient and necessary condition is presented for the existence of a Nash equilibrium in n-person noncooperative games in normal form where strategy sets are not necessarily convex. Under the convexity condition, we show that this new sufficient and necessary condition is a particular case of diagonal transfer quasiconcavity. The result is illustrated with an application to an economy with multilateral environmental externalities and to the existence of a Cournot equilibrium.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://my.ieseg.fr/bienvenue/DownloadDoc.asp?Fich=505085865_2008-ECO-13_Nessah_Kerstens.pdf
File Function: First version, 2008
Download Restriction: no

Paper provided by IESEG School of Management in its series Working Papers with number 2008-ECO-13.

as
in new window

Length: 17 pages
Date of creation: Sep 2008
Date of revision:
Handle: RePEc:ies:wpaper:e200813
Contact details of provider: Postal: 3, rue de la Digue, FR-59000 Lille
Phone: +33/320545892
Fax: +33/320574855
Web page: http://www.ieseg.fr/

More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Nishimura, Kazuo & Friedman, James, 1981. "Existence of Nash Equilibrium in n Person Games without Quasi-Concavity," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(3), pages 637-48, October.
  2. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
  3. Chander, P. & Tulkens, H., . "The core of an economy with multilateral environmental externalities," CORE Discussion Papers RP -1276, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Xu, Yongsheng & Yoshihara, Naoki, 2006. "Alternative characterizations of three bargaining solutions for nonconvex problems," Games and Economic Behavior, Elsevier, vol. 57(1), pages 86-92, October.
  5. CHANDER, Parkash, . "The gamma-core and coalition formation," CORE Discussion Papers RP -1993, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. M. J. Farrell, 1959. "The Convexity Assumption in the Theory of Competitive Markets," Journal of Political Economy, University of Chicago Press, vol. 67, pages 377.
  7. Scarf, Herbert E, 1981. "Production Sets with Indivisibilities-Part I: Generalities," Econometrica, Econometric Society, vol. 49(1), pages 1-32, January.
  8. Vives, X., 1988. "Nash Equilibrium With Strategic Complementarities," UFAE and IAE Working Papers 107-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  9. Baye, Michael R & Tian, Guoqiang & Zhou, Jianxin, 1993. "Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-quasiconcave Payoffs," Review of Economic Studies, Wiley Blackwell, vol. 60(4), pages 935-48, October.
  10. Conley, John P. & Wilkie, Simon, 1996. "An Extension of the Nash Bargaining Solution to Nonconvex Problems," Games and Economic Behavior, Elsevier, vol. 13(1), pages 26-38, March.
  11. Lin Zhou, 1997. "The Nash Bargaining Theory with Non-Convex Problems," Econometrica, Econometric Society, vol. 65(3), pages 681-686, May.
  12. Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 1-26, January.
  13. Peter Bogetoft, 1994. "Incentive Efficient Production Frontiers: An Agency Perspective on DEA," Management Science, INFORMS, vol. 40(8), pages 959-968, August.
  14. Wilson, Robert, 1997. "Nonlinear Pricing," OUP Catalogue, Oxford University Press, number 9780195115826, March.
  15. Starrett, David A., 1972. "Fundamental nonconvexities in the theory of externalities," Journal of Economic Theory, Elsevier, vol. 4(2), pages 180-199, April.
  16. Scarf, Herbert E, 1981. "Production Sets with Indivisibilities-Part II: The Case of Two Activities," Econometrica, Econometric Society, vol. 49(2), pages 395-423, March.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:ies:wpaper:e200813. 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: (Monika Marin)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.