IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v59y2010i3p282-287.html
   My bibliography  Save this article

On the Arrow-Hahn utility representation method

Author

Listed:
  • Gori, Michele
  • Pianigiani, Giulio

Abstract

In this paper we characterize metric spaces used in Beardon's generalization of Arrow-Hahn utility representation method as generalized Peano continua. For continuous preference relations defined on such metric spaces, we further construct an upper semi-continuous utility function which explicitly depends on the distance.

Suggested Citation

  • Gori, Michele & Pianigiani, Giulio, 2010. "On the Arrow-Hahn utility representation method," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 282-287, May.
    • Handle: RePEc:eee:matsoc:v:59:y:2010:i:3:p:282-287
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165-4896(09)00105-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Jose C. R. Alcantud & Ghanshyam B. Mehta, 2005. "Constructive Utility Functions on Banach spaces," Microeconomics 0502003, University Library of Munich, Germany.
    2. Candeal, Juan C. & Indurain, Esteban & Mehta, Ghanshyam B., 2004. "Utility functions on locally connected spaces," Journal of Mathematical Economics, Elsevier, vol. 40(6), pages 701-711, September.
    3. Monteiro, Paulo Klinger, 1987. "Some results on the existence of utility functions on path connected spaces," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 147-156, April.
    4. A. F. Beardon, 1997. "Utility representation of continuous preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(2), pages 369-372.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Campion, Maria J. & Candeal, Juan C. & Indurain, Esteban, 2006. "The existence of utility functions for weakly continuous preferences on a Banach space," Mathematical Social Sciences, Elsevier, vol. 51(2), pages 227-237, March.
    2. O'Callaghan, Patrick, 2016. "Measuring utility without mixing apples and oranges and eliciting beliefs about stock prices," MPRA Paper 69363, University Library of Munich, Germany.
    3. Charalambos Aliprantis & Kim Border & Owen Burkinshaw, 1996. "Market economies with many commodities," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 19(1), pages 113-185, March.
    4. Carlos Alós-Ferrer & Klaus Ritzberger, 2015. "On the characterization of preference continuity by chains of sets," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 115-128, October.
    5. Toranzo, Margarita Estevez & Beloso, Carlos Herves, 1995. "On the existence of continuous preference orderings without utility representations," Journal of Mathematical Economics, Elsevier, vol. 24(4), pages 305-309.
    6. Dino Borie, 2012. "Social Decision Theory and Non-strategic Behaviour," GREDEG Working Papers 2012-10, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    7. Jacques Durieu & Hans Haller & Nicolas Querou & Philippe Solal, 2008. "Ordinal Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 177-194.
    8. Elvio Accinelli, 1999. "Existence of GE: Are the Cases of Non Existence a Cause of Serious Worry?," Documentos de Trabajo (working papers) 0999, Department of Economics - dECON.
    9. Jose C. R. Alcantud & Ghanshyam B. Mehta, 2005. "Constructive Utility Functions on Banach spaces," Microeconomics 0502003, University Library of Munich, Germany.
    10. Bosi, Gianni & Candeal, Juan Carlos & Indurain, Esteban, 2000. "Continuous representability of homothetic preferences by means of homogeneous utility functions," Journal of Mathematical Economics, Elsevier, vol. 33(3), pages 291-298, April.
    11. Beardon, Alan F. & Candeal, Juan C. & Herden, Gerhard & Indurain, Esteban & Mehta, Ghanshyam B., 2002. "The non-existence of a utility function and the structure of non-representable preference relations," Journal of Mathematical Economics, Elsevier, vol. 37(1), pages 17-38, February.
    12. Gutiérrez, José Manuel, 2009. "A characterization of compactness through preferences," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 131-133, January.
    13. Lumley, Thomas & Gillen, Daniel L., 2016. "Characterising transitive two-sample tests," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 118-123.
    14. Inoue, Tomoki, 2010. "A utility representation theorem with weaker continuity condition," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 122-127, January.
    15. Arias de Reyna, Juan & Estévez Toranzo, Margarita & Hervés Beloso, Carlos, 1993. "On non representable preferences," UC3M Working papers. Economics 2894, Universidad Carlos III de Madrid. Departamento de Economía.
    16. Estévez Toranzo, Margarita & Hervés Beloso, Carlos & López López, Miguel A., 1993. "Una nota sobre la representación numérica de relaciones de preferencia," DES - Documentos de Trabajo. Estadística y Econometría. DS 2941, Universidad Carlos III de Madrid. Departamento de Estadística.
    17. Toranzo, Margarita Estevez & Garcia-Cutrin, Javier & Lopez Lopez, Miguel A., 1995. "A note on the representation of preferences," Mathematical Social Sciences, Elsevier, vol. 29(3), pages 255-262, June.
    18. Mabrouk, Mohamed, 2009. "On the extension of a preorder under translation invariance," MPRA Paper 15407, University Library of Munich, Germany.
    19. Mehta, Ghanshyam B. & Monteiro, Paulo Klinger, 1996. "Infinite-dimensional utility representation theorems," Economics Letters, Elsevier, vol. 53(2), pages 169-173, November.
    20. Rustichini, Aldo & Siconolfi, Paolo, 2014. "Dynamic theory of preferences: Habit formation and taste for variety," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 55-68.

    More about this item

    Keywords

    Preference relation Utility function Convex metric space Generalized Peano continuum;

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matsoc:v:59:y:2010:i:3:p:282-287. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505565 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.