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FINITE-DEGREE UTILITY INDEPENDENCE.
- Source :
- Mathematics of Operations Research; Aug82, Vol. 7 Issue 3, p348-353, 6p
- Publication Year :
- 1982
-
Abstract
- When u is a von Neumann-Morgenstern utility function on X ⊗ Y. Y is ‘utility independent’ of X if u can be written as u(x, y)=f(x)g(y) + a(x) with f positive. This paper introduces a fundamental extension of utility independence that is base on induced indifference relations over gambles on one factor when the level of the other factor is fixed. It is proved that Y is ‘degree-n utility independent’ of X if and only if u can be written as u(x, y)= f<subscript>1</subscript>(x)g<subscript>1</subscript>(y)+ … + f<subscript>n</subscript>(x)g<subscript>n</subscript>(y)+ a(x) and cannot be written in a similar way with fewer than n products of single-factor functions. A similar theorem holds when the roles of Y and X are interchanged. It follows that if Y is degree-n utility independent of X, then X is degree-m utility independent of Y for some m ∈ ¦ n - l . n . n + l ¦; it is then shown that u can be represented in terms of n conditional utility functions on Y . m conditional utility functions on X, and at most (n + l)(m + 1) scaling constants. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0364765X
- Volume :
- 7
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Mathematics of Operations Research
- Publication Type :
- Academic Journal
- Accession number :
- 9280270
- Full Text :
- https://doi.org/10.1287/moor.7.3.348