More Strategies, More Nash Equilibria
This short paper isolates a non-trivial class of games for which there exists a monotone relation between the size of pure strategy spaces and the number of pure Nash equilibria (Theorem). This class is that of two-player nice games, i.e., games with compact real intervals as strategy spaces and continuous and strictly quasi-concave payoff functions, assumptions met by many economic models. We then show that the sufficient conditions for Theorem to hold are tight.
|Date of creation:||Feb 2005|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: (618) 8303 5540
Web page: http://www.economics.adelaide.edu.au/
More information through EDIRC
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.:
- McLennan, A., 1999.
"The Expected Number of Nash Equilibria of a Normal Form Game,"
306, Minnesota - Center for Economic Research.
- Andrew McLennan, 2005. "The Expected Number of Nash Equilibria of a Normal Form Game," Econometrica, Econometric Society, vol. 73(1), pages 141-174, 01.
- Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1, December.
- McLennan, Andrew & Berg, Johannes, 2005. "Asymptotic expected number of Nash equilibria of two-player normal form games," Games and Economic Behavior, Elsevier, vol. 51(2), pages 264-295, May.
- Bernheim, B Douglas & Whinston, Michael D, 1998.
"Incomplete Contracts and Strategic Ambiguity,"
American Economic Review,
American Economic Association, vol. 88(4), pages 902-32, September.
- B. Douglas Bernheim & Michael D. Whinston, 1997. "Incomplete Contracts and Strategic Ambiguity," Harvard Institute of Economic Research Working Papers 1787, Harvard - Institute of Economic Research.
- Von Stengel, Bernhard, 2002. "Computing equilibria for two-person games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 45, pages 1723-1759 Elsevier.
- Gossner, Olivier, 2010. "Ability and knowledge," Games and Economic Behavior, Elsevier, vol. 69(1), pages 95-106, May.
- McKelvey, Richard D. & McLennan, Andrew, 1996. "Computation of equilibria in finite games," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 2, pages 87-142 Elsevier.
- Thomas Quint & Martin Shubik, 1994. "On the Number of Nash Equilibria in a Bimatrix Game," Cowles Foundation Discussion Papers 1089, Cowles Foundation for Research in Economics, Yale University.
When requesting a correction, please mention this item's handle: RePEc:adl:wpaper:2005-01. 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: (Dmitriy Kvasov)
If references are entirely missing, you can add them using this form.