Utility Functions Invariant with Respect to Some Classes of Shifts

J. Chudziak Department of Mathematics, University of Rzeszów, T. Rejtana 16A, 35-959 Rzeszów, Poland

Full Text PDF

A utility function U is said to be invariant with respect to a family of transformations Γp provided, for every member γ of Γp, U and Uırc γ represent the same preference relation over lotteries. An invariance with respect to a wide class of transformations can be reduced to an invariance with respect to the shift transformations. We give a complete answer to the following question: given a nonempty set T of shifts determine all utility functions invariant with respect to the shift transformations by every element of T. As a consequence of our results we obtain the forms of utility functions invariant with respect to the families of commuting transformations.

DOI: 10.12693/APhysPolA.123.508 PACS numbers: 89.65.Gh