The Existence and Uniqueness of Equilibria in Convex Games with Strategies in Hilbert Spaces
In this paper we extend the approach of Rosen  for existence and uniqueness of Nash equilibria for finite-dimensional convex games to an abstract setting in which the strategies of each player are in separable Hilbert spaces. Through the use of an extension of the Kakutani fixed-point theorem, we are able to extend Rosen’s existence result to this setting. Our uniqueness results are obtained by extending Rosen’s notion of strict diagonal convexity to this setting. Several examples, in the context of open-loop dynamic games, to which our results may be applied are presented.
KeywordsNash Equilibrium Feasible Point Separable Hilbert Space Constraint Qualification Dynamic Game
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