The Existence of Equilibria in Discontinuous and Nonconvex Games

Rabia Nessah () and Guoqiang Tian

No 2008-ECO-14, Working Papers from IESEG School of Management

Abstract: This paper investigates the existence of pure strategy, dominant-strategy, and mixed strategy Nash equilibria in discontinuous and nonconvex games. We introduce a new notion of very weak continuity, called weak transfer continuity, which holds in a large class of discontinuous economic games and is easy to check. We show that it, together with the compactness of strategy space and the quasiconcavity of payoff functions, permits the existence of pure strategy Nash equilibria. Our equilibrium existence result neither implies nor is implied by the existing results in the literature such as those in Baye et al. [1993] and Reny [1999]. We provide sufficient conditions for weak transfer continuity by introducing notions of weak transfer upper continuity and weak transfer lower continuity. These conditions are satisfied in many economic games and are often quite simple to check. We also introduce the notion of weak dominant transfer upper continuity, and use it to study the existence of dominant strategy equilibria. We then generalize these results and those in Baye et al. [1993] and Reny [1999] without assuming any form of quasi-concavity of payoff functions or convexity of strategy spaces.

Keywords: Nash equilibrium; dominant strategy equilibrium; discontinuity; nonquasiconcavity; nonconvexity and mixed strategy (search for similar items in EconPapers)
Pages: 34 pages
Date: 2008-11, Revised 2010-03
New Economics Papers: this item is included in nep-gth and nep-mic
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://my.ieseg.fr/bienvenue/DownloadDoc.asp?Fich= ... _Nessah_Guoqiang.pdf First version, 2009 (application/pdf)
Our link check indicates that this URL is bad, the error code is: 403 FORBIDDEN (http://my.ieseg.fr/bienvenue/DownloadDoc.asp?Fich=103380412_2008-ECO-14_1_Nessah_Guoqiang.pdf [301 Moved Permanently]--> https://my.ieseg.fr/bienvenue/DownloadDoc.asp?Fich=103380412_2008-ECO-14_1_Nessah_Guoqiang.pdf [301 Moved Permanently]--> https://iesegnet.sharepoint.com/sites/Intranet-Home/bienvenue/DownloadDoc.asp?Fich=103380412_2008-ECO-14_1_Nessah_Guoqiang.pdf)
http://my.ieseg.fr/bienvenue/DownloadDoc.asp?Fich= ... O-11_Nessah_Tian.pdf Revised version, 2010 (application/pdf)
Our link check indicates that this URL is bad, the error code is: 403 FORBIDDEN (http://my.ieseg.fr/bienvenue/DownloadDoc.asp?Fich=230987794_2010-ECO-11_Nessah_Tian.pdf [301 Moved Permanently]--> https://my.ieseg.fr/bienvenue/DownloadDoc.asp?Fich=230987794_2010-ECO-11_Nessah_Tian.pdf [301 Moved Permanently]--> https://iesegnet.sharepoint.com/sites/Intranet-Home/bienvenue/DownloadDoc.asp?Fich=230987794_2010-ECO-11_Nessah_Tian.pdf)

Related works:
Working Paper: Existence of Equilibria in Discontinuous and Nonconvex Games (2009)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ies:wpaper:e200814

Access Statistics for this paper

More papers in Working Papers from IESEG School of Management Contact information at EDIRC.
Bibliographic data for series maintained by Lies BOUTEN ().