Archimedeaness and additive utility on totally ordered semigroups |
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| Authors: | J. R. De Miguel J. C. Candeal E. Induráin |
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| Affiliation: | (1) Departamento de Matemática e Informática, Universidad Pública de Navarra, Campus Arrosadía s.n., E-31006 Pamplona, Spain;(2) Departmento de Análisis Económico, Universidad de Zaragoza, Gran Vía 2-4, E-50005 Zaragoza, Spain |
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| Abstract: | We study problems concerning the existence of additive utility funtions defined on totally ordered semigroups. The existence of an additive utility function on a semigroup is characterized by means of conditions that are similar, but not equivalent, to Archimedeaness. This fact is used to analyze the existence of utility representations (not necessarily additive) on totally ordered Abelian groups. In this direction, we show that the positive cone of a representable totally ordered Abelian group admits a countable partition into Archimedean semigroups. All the semigroups in that partition are representable by means of a utility function, but at most one is additively representable. Communicated by M. W. Mislove |
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