The Role of Some Functional Equations in Decision Analysis

Authors:
Ali E. Abbas;János Aczél
Affiliations:
Department of Industrial and Enterprise Systems Engineering, College of Engineering, University of Illinois at Urbana--Champaign, Urbana, Illinois 61801;Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
Venue:
Decision Analysis
Year:
2010

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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.