von Neumann-Morgenstera Utility Functions on Two Attributes

Peter C. Fishburn
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Peter C. Fishburn: The Pennsylvania State University, University Park, Pennsylvania

Operations Research, 1974, vol. 22, issue 1, 35-45

Abstract: Five special forms for a von Neumann-Morgenstern utility function u on a product set A × X are examined. Each expresses u as a combination of functions defined on the separate factors A and X . The five forms include the additive and multiplicative forms, u = u 1 + u 2 and u = f 1 f 2 , respectively, and the additive form with independent product expressed by u = u 1 + u 2 + f 1 f 2 . Necessary and sufficient preference conditions are identified for each form, along with admissible transformations on the single-argument functions.

Date: 1974
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