On Volterra functional operator games on a given set

The paper is devoted to finding sufficient conditions for an ϵ‐equilibrium in the sense of piecewise‐program strategies in antagonistic games associated with nonlinear controlled functional operator equations and cost functionals of a rather general form. The concept of piecewise‐program strategies is defined based on the concept of Volterra set chain for operators involved in equations controlled by opponent players. Reduction of distributed control systems to equations of this type is illustrated by examples.