In the game with nature, the synthetic Wald–Savage criterion is defined as the principle of optimality, which makes possible to evaluate the optimality of strategies from a synthetic (joint) point of view of wins and risks. The definition of the synthesized strategy is given, i.e. a strategy that is optimal by the Wald–Savage criterion and is not optimal by either the Wald criterion or the Savage criterion. Introduced into the property of synthesizing, which consists in the existence of a synthesized strategy. Scientific novelty consists in solving the formulated problem of synthesizing, which consists in finding the necessary and sufficient conditions for the Wald–Savage criterion to have no synthesizing properties. Sufficient conditions are also of practical importance in analyzing the problems of making optimal economic decisions, since the fulfillment of these conditions means that it does not make sense to use the Wald–Savage criterion to find synthesized strategies. Moreover, the verification of sufficient conditions does not require reference to the Wald–Savage criterion itself, but is based only on the component criteria. However, the exploitation of the Wald–Savage criterion in the absence of its synthesis properties is not absolutely useless, since it reveals the dependence of the application of the Wald and Savage criteria on the determined payoff indicator. The application of the obtained results is illustrated on the solution of the problem of economic content on the optimal choice of the technological mode of production.
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Рис. 3. Графики показателей
-оптимальных векторов в случае, когда ломаная, представляющая график функции
, состоит из четырех звеньев