On Stackelberg equilibrium in the sense of program strategies in Volterra functional operator games

Abstract

For a nonlinear Volterra functional operator equation controlled by two players with the help of finite dimensional program controls with integral objective functionals we prove existence of Stackelberg equilibrium (in the style of M.S.Nikol'skiy). On this way we use our formerly proved results on continuous dependence of the state and functionals on finite dimensional controls and also classical Weierstrass theorem. The property of being singleton for the minimizer set of the first player is proved by the scheme of M.S. Nikol'skiy applied earlier for a linear ordinary differential  equation.