411_Pessimism_and_the_Maximin_and_Minimax_Regret_Rules -...

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Topic 4: Decision Analysis Module 4.1: Traditional Decision Theory Lecture 4.1.1: Pessimism and the maximin and minimax regret rules INTRODUCTION Decision theory pertains to human decision making in a world of incomplete information and incomplete human control over events. Decision theory posits two players: a cognitive human and a randomizing nature. The human, called the decision maker, performs analyses, makes calculations, and cognitively decides upon a course of action in an effort to optimize his or her own welfare. The metaphorical nature is non-cognitive, does not perform analyses or make calculations, and does not choose courses of action in any self-interested way. Rather, nature blithely selects courses of action purely in a probabilistic way. Decision Problems The two fundamental concepts of decision theory are states of nature and acts. States of nature are under the control of nature and beyond the control of the decision maker, and are probabilistically selected by nature. Acts are under the control of the decision maker and any one of the available acts can be selected by the decision maker. Further, decision theory presumes that the problem is presented to the decision maker, i.e., that the problem itself, like the states of nature, is beyond the control of the decision maker. A decision problem is represented as a pair <S,A> composed of a set S of states of nature and a set A of acts. So specified, <S,A> is a decision problem under uncertainty . If the decision maker has a probability system over the states, then <S,A> is a decision problem under risk . Decision Makers Decision Theory posits that the human decision maker brings to the resolution of a decision problem beliefs and preferences. Specifically, the theory presumes that the decision maker possesses a probability system that captures his or her (partial) beliefs about nature's selection of states, a belief system about the outcomes accruing to the
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This note was uploaded on 01/03/2011 for the course COMM 290 taught by Professor Brian during the Winter '09 term at The University of British Columbia.

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411_Pessimism_and_the_Maximin_and_Minimax_Regret_Rules -...

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