Theory and Decision

, Volume 53, Issue 1, pp 87-94

First online:

Expected utility from additive utility on semigroups

  • Juan C. CandealAffiliated withDepartamento de Análisis Económico, Universidad de Zaragoza
  • , Juan R. De MiguelAffiliated withDepartamento de Matemática e Informática, Universidad Pública de Navarra
  • , Esteban InduráinAffiliated withDepartamento de Matemática e Informática, Universidad Pública de Navarra Email author 

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In the present paper we study the framework of additive utility theory, obtaining new results derived from a concurrence of algebraic and topological techniques. Such techniques lean on the concept of a connected topological totally ordered semigroup. We achieve a general result concerning the existence of continuous and additive utility functions on completely preordered sets endowed with a binary operation ``+'', not necessarily being commutative or associative. In the final part of the paper we get some applications to expected utility theory, and a representation theorem for a class of complete preorders on a quite general family of real mixture spaces.

Preordered sets utility funtions continuous and additive utility expected utility semigroups