Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Location of Nash equilibria: A Riemannian geometrical approach


Author: Alexandru Kristály
Journal: Proc. Amer. Math. Soc. 138 (2010), 1803-1810
MSC (2000): Primary 91A10, 58B20, 49J40, 49J52, 46N10
Published electronically: December 21, 2009
MathSciNet review: 2587465
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Existence and location of Nash equilibrium points are studied for a large class of a finite family of payoff functions whose domains are not necessarily convex in the usual sense. The geometric idea is to embed these non-convex domains into suitable Riemannian manifolds regaining certain geodesic convexity properties of them. By using recent non-smooth analysis on Riemannian manifolds and a variational inequality for acyclic sets, an efficient location result of Nash equilibrium points is given. Some examples show the applicability of our results.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 91A10, 58B20, 49J40, 49J52, 46N10

Retrieve articles in all journals with MSC (2000): 91A10, 58B20, 49J40, 49J52, 46N10


Additional Information

Alexandru Kristály
Affiliation: Department of Economics, Babeş-Bolyai University, 400591 Cluj-Napoca, Romania
Email: alexandrukristaly@yahoo.com

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10145-4
PII: S 0002-9939(09)10145-4
Keywords: Nash equilibrium point, Riemannian manifold, nonsmooth analysis.
Received by editor(s): January 14, 2009
Published electronically: December 21, 2009
Additional Notes: This work was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences and by PN II IDEI$_$527 of CNCSIS
Communicated by: Peter A. Clarkson
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.