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A generalization of Nash's theorem with higher-order functionals
1School of Electronic Engineering and Computer Science , Queen Mary University of London , London E1 4NS, UK.
Abstract:
The recent theory of sequential games and selection functions by Escardó & Oliva is extended to games in which players move simultaneously. The Nash existence theorem for mixed-strategy equilibria of finite games is generalized to games defined by selection functions. A normal form construction is given, which generalizes the game-theoretic normal form, and its soundness is proved. Minimax strategies also generalize to the new class of games, and are computed by the Berardi-Bezem-Coquand functional, studied in proof theory as an interpretation of the axiom of countable choice.
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