On a Class of Nonlinear Functionals on Spaces of Continuous Functions

This paper is motivated by certain ideas which arise in the theory of differential games (see [3, 41). We abstract the particular features of differential games which are relevant in the notion of a positional game. Suppose S is a topological space, and g is a continuous real-valued function on S. We consider a game between two players, whom we call the maximizer and the minimizer, which falls into two phases.