Decisions with probabilities over finite product spaces

Techniques for decision-making with probabilities over finite product spaces are discussed. In general, the type of decision problem generated by the available probabilistic information is one of decision under partial uncertainty: the probability distribution over the event space for the problem is determined only to the extent that it is contained in a convex polyhedron of distributions. The structure of this set makes computationally feasible the application of any of the various criteria for decision-making with indeterminate probabilities that have appeared in the literature. Algorithms are developed for economically reducing the size of sets guaranteed to contain the unknown distribution over the event space for a given problem, thereby improving the quality of the decision made using any criterion