Generalization of minimax and maximin criteria in a game against nature for the case of a partial a priori uncertainty.

This study proposes a new criterion for choosing the optimal decision in a game against nature under a partial a priori uncertainty. The paper's main novelty consists in examining the situation when a part of the a priori probabilities of states of nature is known, and the other part is unknown. We prove the theorems for choosing the optimal decision as for the payoff and risk matrix, as well as for the profit matrix in the situation of a partial a priori uncertainty.