GEOMETRIC SOLUTION PROBLEMS OF SYNTHESIS BY WALD - SAVAGE CRITERION AND ANNEX TO THE OPTIMAL CHOICE OF TECHNOLOGICAL METHOD FOR PRODUCING PRODUCTS
In the game with nature, the Wald-Savage synthetic criterion, defined by a linear convolution of Wald’s well-known pessimistic criteria regarding winnings and Savage regarding risks, is introduced as an optimality principle. The Wald-Savage criterion makes it possible to evaluate the optimality of the chosen strategies from the synthetic (joint) point of view of gains and risks. A new concept of a synthesized strategy is defined as a strategy that is optimal by the Wald-Savage criterion, but not optimal by either the Wald criterion or the Savage criterion. The problem of synthesizing by the Wald-Savage criterion is formulated, which consists in finding the necessary and sufficient conditions under which there are no synthesized strategies in the game with nature. Under these conditions, the application of the Wald-Savage criterion becomes meaningless, since it leads to unsynthesized strategies that are optimal by the Wald-Savage criterion, which at the same time are optimal by the Wald criterion or Savage criterion. A geometric solution to the synthesis problem by the Wald-Savage criterion is proposed, consisting in a specific arrangement of special points at which this criterion does not have the synthesizing property. The application of the obtained results is illustrated by the analysis of the economic content problem, in which the question of the optimal choice of the technological method of production with the lowest costs is solved.