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Multiattribute Utility Copulas

Department of Industrial and Enterprise Systems Engineering, College of Engineering, University of Illinois at Urbana–Champaign, Urbana, Illinois 61801
aliabbas{at}uiuc.edu

We introduce the notion of a multiattribute utility copula that expresses any (i) continuous; (ii) bounded multiattribute utility function that is (iii) nondecreasing with each of its arguments, and (iv) strictly increasing with each argument for at least one reference value of the complement attributes, in terms of single-attribute utility assessments. This formulation provides a wealth of new functional forms that can be used to model preferences over utility-dependent attributes and enables sensitivity analyses to some of the widely used functional forms of utility independence. We introduce a class of utility copulas, called Archimedean utility copulas, and discuss the conditions under which it yields the additive and multiplicative forms. We also discuss linear and composite transformations of utility copulas that construct utility functions with partial utility independence. We conclude with the risk aversion functions that are induced by utility copula formulations and work through several examples to illustrate the approach.

Subject classifications: utility elicitation; utility dependence; copula; utility copula; multiattribute utility.
History: Received September 2007; revision received April 2008; accepted May 2008.