  The recent theory of sequential games and selection functions by Mar- tin
Escardo and Paulo Oliva is extended to games in which players move
simultaneously. The Nash existence theorem for mixed-strategy equilibria of
finite games is generalised to games defined by selection functions. A normal
form construction is given which generalises the game-theoretic normal form,
and its soundness is proven. Minimax strategies also gener- alise 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.
