A hierarchical game under uncertainty conditions with using player risk function and guarantied strategy estimate

A game-theoretic model of optimal interaction of players in a two-level hierarchic system under uncertainty conditions is proposed. The players keep in mind the outcome with the worst value of the uncertain factor, so that the upper-level player also applies guaranteed approach to the lower-level player. The convergence of the type of penalty function method we use has been proved, the problem of passing from iterated limits by the penalty parameters to the conventional limit by means of their match has been solved. The optimality conditions were obtained.