Existence of a utility on a topological semigroup

Abstract

This paper presents a comprehensive mathematical framework in which a unified treatment of additive and expected utility can be given. For achieving this, elaborate structural assumptions, characterizing a simply ordered, topological semigroup, have to be established in order to construct an isomorphism with the additive group of real numbers. This construction establishes a link between additive and expected utility theory to the extent that the same mathematical considerations leading to the derivation of an additive representation are also valid for proving the expected utility theorem.