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Vietnam Journal of Mathematics 35:2(2007) 201-213  Set-Valued Versions of Nash Equilibria and Ky Fan Inequality in Hyperconvex Metric Spaces Le Anh Dung Abstract.  In this paper we prove the existence of generalized Nash equilibrium points and some versions of Ky Fan inequality for set-valued mappings in hyperconvex metric spaces. From these we obtain a version of Kakutani's fixed point theorem in such spaces.   2000 Mathematics Subject Classification: 47H05, 47H10, 49J40, 53A07. Keywords: U.q-convex (U.q-concave; L.q-convex; L.q-concave) mapping; upper (lower) demicontinuous mapping; generalized Nash equilibrium point.

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