Measure Theoretic Structures for Sequential Decision Models.

by Ralph E. Strauch

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An expository paper dealing with the elements which must be represented in probabilistic models of general state space sequential decision problems. These elements are described, and the ways they are represented in two such models, a dynamic programming model due to Blackwell and a gambling model due to Dubins and Savage, are examined. If the set of possible positions in which the decisionmaker might find himself is uncountable, then a measure theoretic structure connecting the basic elements of the problem is required in order to ensure adequate definitions of the overall dynamics of the problem and the value to the decisionmaker of his overall behavior. The dynamic programming model uses a countably additive measure structure based on metric considerations, while the gambling model uses finitely additive measures defined on all subsets of the basic space. 21 pp. Ref.

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