Feedback Strategies in a Nonzero-Sum Differential Game of Special Type

The paper deals with the construction of universal closed-loop strategies for two-person nonzero-sum differential game of a special type. The dynamics of the first player is defined by its own position and control. The dynamics of the second player is defined by its own control and the position of both players. The strategies are constructed based on the solution of a system of Hamilton-Jacobi equations. The system of Hamilton-Jacobi equations has a hierarchical type. A generalized solution of the system of Hamilton-Jacobi equations belongs to the class of multivalued mappings. We show the relationship between the values of the players and the generalized solution of the system of Hamilton-Jacobi equations.