Advanced Search
MyIDEAS: Login to save this article or follow this journal

On the existence of equilibria in discontinuous games: three counterexamples

Contents:

Author Info

  • Guilherme Carmona

    ()

Abstract

We study whether we can weaken the conditions given in Reny (1999) and still obtain existence of pure strategy Nash equilibria in quasiconcave normal form games, or, at least, existence of pure strategy $\varepsilon-$equilibria for all epsilon>0. We show by examples that there are: (1) quasiconcave, payoff secure games without pure strategy epsilon-equilibria for small enough epsilon>0 (and hence, without pure strategy Nash equilibria), (2) quasiconcave, reciprocally upper semicontinuous games without pure strategy epsilon-equilibria for small enough epsilon>0, and (3) payoff secure games whose mixed extension is not payoff secure. The last example, due to Sion and Wolfe (1957), also shows that non-quasiconcave games that are payoff secure and reciprocally upper semicontinuous may fail to have mixed strategy equilibria.

(This abstract was borrowed from another version of this item.)

Download Info

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://hdl.handle.net/10.1007/s001820400187
Download Restriction: Access to full text is restricted to subscribers.

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Bibliographic Info

Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 33 (2005)
Issue (Month): 2 (06)
Pages: 181-187

as in new window
Handle: RePEc:spr:jogath:v:33:y:2005:i:2:p:181-187

Contact details of provider:
Web page: http://link.springer.de/link/service/journals/00182/index.htm

Order Information:
Web: http://link.springer.de/orders.htm

Related research

Keywords: discontinuous games; payoff security; reciprocal upper semicontinuity; nash equilibrium;

Other versions of this item:

Find related papers by JEL classification:

References

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. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, Econometric Society, vol. 67(5), pages 1029-1056, September.
  2. 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, Wiley Blackwell, vol. 60(4), pages 935-48, October.
  3. Simon, Leo K, 1987. "Games with Discontinuous Payoffs," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 54(4), pages 569-97, October.
  4. Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 53(1), pages 1-26, January.
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 in new window

Cited by:
  1. Nessah, Rabia & Tian, Guoqiang, 2008. "Existence of Equilibria in Discontinuous Games," MPRA Paper 41206, University Library of Munich, Germany, revised Mar 2010.
  2. repec:hal:journl:halshs-00197491 is not listed on IDEAS
  3. Paulo Klinger Monteiro & Frank H. Page Jr, 2005. "Uniform payoff security and Nash equilibrium in metric games," Cahiers de la Maison des Sciences Economiques, Université Panthéon-Sorbonne (Paris 1) b05086, Université Panthéon-Sorbonne (Paris 1).
  4. Monteiro, Paulo Klinger & Page Jr, Frank H., 2007. "Uniform payoff security and Nash equilibrium in compact games," Journal of Economic Theory, Elsevier, vol. 134(1), pages 566-575, May.
  5. Pavlo Prokopovych & Nicholas C. Yannelis, 2012. "On Uniform Conditions for the Existence of Mixed Strategy Equilibria," Discussion Papers 48, Kyiv School of Economics.
  6. Pavlo Prokopovych & Nicholas C.Yannelis, 2013. "On the Existence of Mixed Strategy Nash equilibria," Discussion Papers 50, Kyiv School of Economics.
  7. Luciano Castro, 2011. "Equilibrium existence and approximation of regular discontinuous games," Economic Theory, Springer, vol. 48(1), pages 67-85, September.
  8. Carmona, Guilherme, 2006. "Polyhedral Convexity and the Existence of Approximate Equilibria in Discontinuous Games," FEUNL Working Paper Series wp488, Universidade Nova de Lisboa, Faculdade de Economia.
  9. Rabia Nessah & Guoqiang Tian, 2009. "Existence of Equilibria in Discontinuous and Nonconvex Games," Levine's Working Paper Archive 814577000000000206, David K. Levine.
  10. Pavlo Prokopovych, 2011. "On equilibrium existence in payoff secure games," Economic Theory, Springer, vol. 48(1), pages 5-16, September.
  11. Capraro, Valerio & Scarsini, Marco, 2013. "Existence of equilibria in countable games: An algebraic approach," Games and Economic Behavior, Elsevier, vol. 79(C), pages 163-180.
  12. Philip J. Reny, 2013. "Nash Equilibrium in Discontinuous Games," Working Papers, Becker Friedman Institute for Research In Economics 2013-004, Becker Friedman Institute for Research In Economics.
  13. Oriol Carbonell-Nicolau, 2011. "The Existence of Perfect Equilibrium in Discontinuous Games," Games, MDPI, Open Access Journal, MDPI, Open Access Journal, vol. 2(3), pages 235-256, July.
  14. Rabia Nessah & Guoqiang Tian, 2008. "The Existence of Equilibria in Discontinuous and Nonconvex Games," Working Papers 2008-ECO-14, IESEG School of Management, revised Mar 2010.
  15. Luciano I. de Castro, 2008. "Equilibria Existence in Regular Discontinuous Games," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1463, Northwestern University, Center for Mathematical Studies in Economics and Management Science.

Lists

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

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:spr:jogath:v:33:y:2005:i:2:p:181-187. 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: (Guenther Eichhorn) or (Christopher F Baum).

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.