A generalization of Nash's theorem with higher-order functionals
Julian Hedges · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 2013
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.