Saddle points and active equilibriums in differential games with dependent strategies (Q1594334)

A two-person zero-sum differential game with mixed strategies is considered. The movement equation is also overaged with respect to mixed strategies. The set of admissible pairs of the players' pure strategies is a proper subset of its Cartesian product. In this sense the players' strategies are dependent. The author defines a notion of dependent saddle points as boundary points of the set of active equilibriums. The latter set was defined in the author's previous papers. The necessary conditions for the existence of a dependent saddle point and for the optimality of a boundary point of the set of active equilibriums are given.