Playing in a combination of risk and uncertainty

Abstract

The problem of determining the optimal strategy under conflict conditions is considered. The subject of research is a game with nature in conditions of a combination of risk and uncertainty. Two situations are considered. First, the probability of states of nature is not affected by strategies. Second, the probability depends on strategies. The game matrix is reduced to a two-block matrix. The first block contains wins for which the probabilities of states of nature are known, while the second block contains wins with uncertain states. For each strategy, the arithmetic mean wins are calculated in the first and second blocks, while the principle of Laplace's insufficient basis is used for the second block. The optimal strategy is determined by the Wald criterion, which achieves the maximum value of the arithmetic mean wins for both blocks. When calculating the criterion, the arithmetic means of the second block are weighted by the probability of the occurrence of uncertain states of nature. It is proved that the ranking of strategies using the Bayes criterion depends on the probability of the occurrence of uncertain states of nature.