Nash Equilibria over Hausdorff Spaces

Edgard Almeida Pimentel, Juliana Fernandes da Silva
The aim of this paper is to introduce Nash Equlibrium theorem for finite dimensional vector spaces along with Kakutani's fixed point result, which is a crucial step in the former's strablishment. Closely following Glicksberg's fixed point theorem, we then present a generalization of Kakutani's one for the context of locally convex Hausdorff spaces which culminates to a broader statement of Nash Equilibrium theorem, envolving games whose pure strategies finite sets are contained in Hausdorff topological spaces.
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