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Numerical Representation Of Acyclic Preferences

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  • Begoña Subiza Martínez

    () (Universidad de Alicante)

Abstract

In this paper, it is shown that, under certain conditions on a preference relation defined on a set X, there exists a numerical representation by means of set-valued real functions. This kind of representation extends the usual utility function as well as the representation by means of two real functions. The continuity of this representation is also discussed.

Suggested Citation

  • Begoña Subiza Martínez, 1993. "Numerical Representation Of Acyclic Preferences," Working Papers. Serie AD 1993-09, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  • Handle: RePEc:ivi:wpasad:1993-09
    as

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    File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-1993-09.pdf
    File Function: Fisrt version / Primera version, 1993
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    References listed on IDEAS

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    1. Begoña Subiza Martínez & Carmen Herrero Blanco, 1991. "A characterization of acyclic preferences on countable sets," Working Papers. Serie AD 1991-01, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    2. Chateauneuf, Alain, 1987. "Continuous representation of a preference relation on a connected topological space," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 139-146, April.
    3. Chakravorty, Bhaskar & Corchon, Luis C. & Wilkie, Simon, 2006. "Credible implementation," Games and Economic Behavior, Elsevier, vol. 57(1), pages 18-36, October.
    4. Luis Corchón & Simon Wilkie, 1990. "Doubly implementing the ratio correspondence with a "natural" mechanism," Working Papers. Serie AD 1990-03, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    5. Bridges, Douglas S., 1983. "Numerical representation of intransitive preferences on a countable set," Journal of Economic Theory, Elsevier, vol. 30(1), pages 213-217, June.
    6. Fishburn, P. C., 1983. "Utility functions on ordered convex sets," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 221-232, December.
    7. Peleg, Bezalel, 1970. "Utility Functions for Partially Ordered Topological Spaces," Econometrica, Econometric Society, vol. 38(1), pages 93-96, January.
    8. Herrero, Carmen & Villar, Antonio, 1991. "Vector mappings with diagonal images," Mathematical Social Sciences, Elsevier, vol. 22(1), pages 57-67, August.
    9. Mirman, Leonard J & Samuelson, Larry & Urbano, Amparo, 1993. "Monopoly Experimentation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(3), pages 549-563, August.
    10. Corchon, Luis C., 1991. "Oligopolistic competition among groups," Economics Letters, Elsevier, vol. 36(1), pages 1-3, May.
    11. Bridges, Douglas S., 1983. "A numerical representation of preferences with intransitive indifference," Journal of Mathematical Economics, Elsevier, vol. 11(1), pages 25-42, January.
    12. Marhuenda, F, 1995. "Distribution of Income and Aggregation of Demand," Econometrica, Econometric Society, vol. 63(3), pages 647-666, May.
    13. Carmen Herrero Blanco & José Manuel Gutiérrez Díez, 1990. "Lagrangean conditions for general optimization problems with applications to consumer theory," Working Papers. Serie AD 1990-02, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    14. Begoña Subiza Martínez & Carmen Herrero Blanco, 1992. "Numerical representation of partial orderings," Working Papers. Serie AD 1992-03, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
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    Citations

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    Cited by:

    1. Marc-Arthur Diaye & Michal Wong-Urdanivia, 2006. "A simple test of Richter-rationality," Post-Print halshs-00084390, HAL.
    2. Leobardo Plata-Perez, 2004. "A numerical representation of acyclic preferences when non-comparability and indifference are concepts with different meaning," EconoQuantum, Revista de Economia y Negocios, Universidad de Guadalajara, Centro Universitario de Ciencias Economico Administrativas, Departamento de Metodos Cuantitativos y Maestria en Economia., vol. 1(0), pages 17-23, Enero - J.
    3. Marc-Arthur Diaye & Michal Wong-Urdanivia, 2005. "A simple test of Richter-rationality," Cahiers de la Maison des Sciences Economiques b06008, Université Panthéon-Sorbonne (Paris 1).
    4. Marc-Arthur Diaye & Michal Wong-Urdanivia, 2006. "A Simple Test of Richter-Rationality," Documents de recherche 06-01, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
    5. Martín Browning, 1993. "Dual approaches to utility," Working Papers. Serie AD 1993-10, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    6. José Alcalde, 1994. "Exchange-proofness or divorce-proofness? Stability in one-sided matching markets," Review of Economic Design, Springer;Society for Economic Design, vol. 1(1), pages 275-287, December.
    7. Diaye, Marc-Arthur, 1999. "Variable intervals model," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 21-33, July.
    8. Alejandro Islas-Camargo & Willy W. Cortez, 2004. "Convergencia salarial entre las principales ciudades mexicanas: Un analisis de cointegracion," EconoQuantum, Revista de Economia y Negocios, Universidad de Guadalajara, Centro Universitario de Ciencias Economico Administrativas, Departamento de Metodos Cuantitativos y Maestria en Economia., vol. 1(0), pages 25-47, Enero - J.

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