Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Location of Nash equilibria: A Riemannian geometrical approach

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

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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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