Domain L-Majorization and Equilibrium Existence in Discontinuous Games
We study the equilibrium existence problem in normal form and qualitative games in which it is possible to associate with each nonequilibrium point an open neighborhood and a collection of deviation strategies such that, at any nonequilibrium point of the neighborhood, a player can increase her payoff by switching to the deviation strategy designated for her. An equilibrium existence theorem for compact, quasiconcave games with two players is established. We propose a new form of the better-reply security condition, called the strong single deviation property, that covers games whose set of Nash equilibria is not necessarily closed. We introduce domain L-majorized correspondences and use them to study equilibrium existence in qualitative games.
|Date of creation:||Jul 2010|
|Date of revision:||May 2011|
|Note:||Revised and resubmitted to Economic Theory|
|Contact details of provider:|| Postal: |
Web page: http://www.kse.org.ua/Email:
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.:
- Bagh, Adib, 1998. "Equilibrium in abstract economies without the lower semi-continuity of the constraint maps," Journal of Mathematical Economics, Elsevier, vol. 30(2), pages 175-185, September.
- Luciano I. de Castro, 2008. "Equilibria Existence in Regular Discontinuous Games," Discussion Papers 1463, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Guilherme Carmona, 2011. "Understanding some recent existence results for discontinuous games," Economic Theory, Springer, vol. 48(1), pages 31-45, September.
- 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.
- Pavlo Prokopovych, 2011. "On equilibrium existence in payoff secure games," Economic Theory, Springer, vol. 48(1), pages 5-16, September.
- Yannelis, Nicholas C. & Prabhakar, N. D., 1983. "Existence of maximal elements and equilibria in linear topological spaces," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 233-245, December.
- 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.
When requesting a correction, please mention this item's handle: RePEc:kse:dpaper:31. 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: (Iryna Sobetska)
If references are entirely missing, you can add them using this form.