An approach to the solutions construction in control problems with many decision makers

Two following problems are very important in the nonantagonistic positional differential games theory. The first one is the problem of adequate defining of solution concept. The second one is connected with nonuniqueness of solutions. In this paper we suggest a new approach to constructing of solutions in the control problems with two decision makers. The approach is based on using of the principle of non-aggravation of guaranteed results for both players along trajectories generated by solutions, on using of the rule of maximal displacement in the direction of Pareto optimal states which are the best for one and another players, and, finally, on using of a procedure based on Nash equilibria for a family of special auxiliary bimatrix games.