With this jubilee contribution to the 90th birthday of L. S. Pontryagin the author introduces a rather novel game-theoretic concept of optimal control of stochastic dynamical systems under conditions of incomplete information. Dispensing with proofs, he applies this concept to the stability of a motion x(t), where x is generated as the solution of a stochastic system under the influence of mixed strategies of control and disturbance. This contribution is an informative complement to the last chapter of the monograph of A. A. and N. N. Krasovskiĭ [Control under lack of information, Birkhäuser Boston, Boston, MA, 1995].