On One Differential Game with Payoff Functions of the Germeier Convolution Type

Abstract

The paper considers a differential game model with functionals represented by a convolution in the form of the minimum of two criteria, one of which describes the competition of players in a common (external) sphere of activity and the other describes the personal achievements of each player (in the internal sphere). The player’s control is the resource redistribution between the external and internal spheres. It is shown that, under some natural assumptions of monotonicity of criteria in such games, Nash and Stackelberg equilibria exist and coincide, possessing the properties of stability and Pareto optimality.