title: A generalization of Nash's theorem with higher-order functionals.
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.
authors.affiliation: School of Electronic Engineering and Computer Science , Queen Mary University of London , London E1 4NS, UK.
authors.forename: Julian
authors.initials: J
authors.lastname: Hedges
keywords: Nash equilibrium; higher-order function; normal-form game; selection function