Some Functional Equations Connected with the Utility of Gains and Losses

Abstract

The behavioral properties shown by people when they make selections between different choices will be studied. Based on empirical and logical data a mathematical axiomatic model is built. D. Luce is a major contributor in this area. This thesis is based on his works and those of his many co-authors. Three approaches will be considered that lead to the rank-dependent utility representation of binary gambles composed only of gains (losses) relative to a status quo. The proofs involve the theory of functional equations which is a very powerful tool giving the precise numerical representations.