On various criteria of optimality in probabilistic decision-making

There are two possibilities how to define the optimality of a decision function-with respect to a given set of distributions-in ‘local’ and ‘global’ senses, applying the minimax rule. But an optimal decision function in any of these senses need not be the optimal one for any distribution in this set. It is shown, using linear programming methods, how to find out whether the global minimax decision function is optimal or not. A suitable representation of the decision function is found-in the latter case-on the base of a barycenter concept.