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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
DOI: https://doi.org/10.1090/S0002-9939-09-10145-4
Published electronically: December 21, 2009
MathSciNet review: 2587465
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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.


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Additional Information

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

DOI: https://doi.org/10.1090/S0002-9939-09-10145-4
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.

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