On a competition problem under uncertainty and risks

A hierarchical model of the problem of competition between two firms under the influence of uncertain factors is considered. Two companies produce and supply the same type of products to the market. In addition, products of the same type produced by the importing company enter the market. Moreover, only possible limits are known about the amount of imported goods, which plays the role of uncertainty. The following principles are used: the Wald principle, according to which the player uses a strategy that guarantees him the best outcome in the worst situation, and the Savage principle, according to which the player minimizes his regret, i.e. the difference between what he could get in the game if the outcome was favorable for him, and what he actually got. The optimal strategies of the second player within each approach are indicated. The optimal strategies of the first player are determined depending on the behavior of the second player and his own optimality criterion. The article analyzes the methods of formalizing the optimal solution for the upper-level conflict participant (center), as well as the individual attitude of the second lower-level player (agent) to risk. Sufficient conditions of existence have been found for the presented solutions of the game and their explicit form has been found.