Universal solution in a nonantagonistic positional differential game with vector performance indexes

A concept of solution of the positional differential many players game with vector performance indexes is given. The game is considered in the form extended with respect to the normal form. In particular, one of the additional elements of the game represents a formal description of possibilities of players and coalitions of players concerning their deviations from the solution of the game. Another element describes a response of the remaining players to this deviation. Special binary preference relations of sets and finite collections of sets are used to compare various results in the game. The structure of the introduced solutions of the game is described. An illustrating example is considered.