Nash Equilibria via Duality and Homological Selection

Details Nash Equilibria via Duality and Homological Selection Nash Equilibria via Duality and Homological Selection

2011-11-03

arxiv.org/abs/1111.0754v2

Mathematics

Algebraic Topology

14 pages, 1 figure

Scientific paper

Cost functions in problems concerning the existence of Nash Equilibria are traditionally multilinear in the mixed strategies. The main aim of this paper is to relax the hypothesis of multilinearity. We use basic intersection theory, Poincar\'e Duality and the Dold-Thom Theorem to establish existence of Nash Equilibria under fairly general hypotheses. The Dold-Thom Theorem provides us with a homological version of a selection Theorem, which may be of independent interest.

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