Considering risk attitude in a value of information problem
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In many decisions, one of the available alternatives is to gather more information about the situation at hand, which incurs a cost but leads to a more informed and thus improved decision. Thus, the decision problem is two-fold: first, whether or not to gather additional information, and second, which course of action or design to select based on the available information as a result of the first decision. Such problems are Value of Information problems, which seek to quantify the value of the potential information to guide the decision maker on whether or not it is worthwhile. However, approaches to Value of Information problems typically implicitly assume that the decision maker is risk neutral, in the formulation of the problem. This paper considers how the inclusion of risk attitude affects a decision maker's decision about whether or not additional information is worthwhile. This leads to a more accurate model of decision problems typically facing decision makers. It discusses some of the mathematical complexities and illustrates the problem with an engineering example.
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