The role of some functional equations in decision analysis

The role of some functional equations in decision analysis

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Article ID: iaor20104816
Volume: 7
Issue: 2
Start Page Number: 215
End Page Number: 228
Publication Date: Jun 2010
Journal: Decision Analysis
Authors: ,
Abstract:

This paper presents some functional equations that have played an essential role in the characterization of utility and probability functions in decision analysis. We survey some previous results with improvements and derive several new results. We also discuss some simple methods for the solution of these equations and highlight some subtle points about their use. We show that one functional equation can determine several unknown functions within it, and that relaxing differentiability and requiring only continuity of the functions leads to generalizations of many well-known results in utility and Bayesian probability theory.

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