von Neumann-Morgenstera Utility Functions on Two Attributes

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.