Distribution of pure Nash equilibria in n-person games with random best replies
AbstractIn this paper we study the number of pure strategy Nash equilibria in large finite n-player games. A distinguishing feature of our study is that we allow general - potentially multivalued - best reply correspondences. Given the number K of pure strategies to each player, we assign to each player a distribution over the number of his pure best replies against each strategy profile of his opponents. If the means of these distributions have a limit (mu)i for each player i as the number K of pure strategies goes to infinity, then the limit number of pure equilibria is Poisson distributed with a mean equal to the product of the limit means (mu)i. In the special case when all best reply mappings are equally likely, the probability of at least one pure Nash equilibrium approaches one and the expected number of pure Nash equilibria goes to infinity.
Download InfoIf 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.
Bibliographic InfoPaper provided by Aboa Centre for Economics in its series Discussion Papers with number 71.
Date of creation: Dec 2011
Date of revision:
random games; pure Nash equilibria; n players;
Find related papers by JEL classification:
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-05-02 (All new papers)
- NEP-GTH-2012-05-02 (Game Theory)
- NEP-HPE-2012-05-02 (History & Philosophy of Economics)
- NEP-MIC-2012-05-02 (Microeconomics)
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.:
- Andrew McLennan, 2005.
"The Expected Number of Nash Equilibria of a Normal Form Game,"
Econometric Society, vol. 73(1), pages 141-174, 01.
- McLennan, A., 1999. "The Expected Number of Nash Equilibria of a Normal Form Game," Papers 306, Minnesota - Center for Economic Research.
- Stanford, William, 1997. "On the distribution of pure strategy equilibria in finite games with vector payoffs," Mathematical Social Sciences, Elsevier, vol. 33(2), pages 115-127, April.
- Bade, Sophie & Haeringer, Guillaume & Renou, Ludovic, 2007.
"More strategies, more Nash equilibria,"
Journal of Economic Theory,
Elsevier, vol. 135(1), pages 551-557, July.
- Sophie Bade & Guillaume Haeringer & Ludovic Renou, 2005. "More Strategies, More Nash Equilibria," School of Economics Working Papers 2005-01, University of Adelaide, School of Economics.
- Sophie Bade & Guillaume Haeringer & Ludovic Renou, 2005. "More strategies, more Nash equilibria," Game Theory and Information 0502001, EconWPA.
- Powers, Imelda Yeung, 1990. "Limiting Distributions of the Number of Pure Strategy Nash Equilibria in N-Person Games," International Journal of Game Theory, Springer, vol. 19(3), pages 277-86.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Aleksandra Maslowska).
If references are entirely missing, you can add them using this form.