IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v57y2009i1p131-133.html
   My bibliography  Save this article

A characterization of compactness through preferences

Author

Listed:
  • Gutiérrez, José Manuel

Abstract

The existence of an optimal solution of the standard decision problem can characterize the compactness of the feasible set. It is proved that the feasible set is compact if and only if there is a maximal element for any upper semicontinuous preference. Here "preference" means asymmetric and negatively transitive binary relation.

Suggested Citation

  • Gutiérrez, José Manuel, 2009. "A characterization of compactness through preferences," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 131-133, January.
    • Handle: RePEc:eee:matsoc:v:57:y:2009:i:1:p:131-133
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165-4896(08)00083-8
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    References listed on IDEAS

    as
    1. 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.
    2. Bergstrom, Theodore C., 1975. "Maximal elements of acyclic relations on compact sets," Journal of Economic Theory, Elsevier, vol. 10(3), pages 403-404, June.
    3. Walker, Mark, 1977. "On the existence of maximal elements," Journal of Economic Theory, Elsevier, vol. 16(2), pages 470-474, December.
    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. Subiza, Begona & Peris, Josep E., 1997. "Numerical representation for lower quasi-continuous preferences," Mathematical Social Sciences, Elsevier, vol. 33(2), pages 149-156, April.
    2. 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.
    3. Llinares, Juan-Vicente, 1998. "Unified treatment of the problem of existence of maximal elements in binary relations: a characterization," Journal of Mathematical Economics, Elsevier, vol. 29(3), pages 285-302, April.
    4. Nehring, Klaus, 1996. "Maximal elements of non-binary choice functions on compact sets," Economics Letters, Elsevier, vol. 50(3), pages 337-340, March.
    5. Kukushkin, Nikolai S., 2008. "Maximizing an interval order on compact subsets of its domain," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 195-206, September.
    6. Kukushkin, Nikolai S., 2018. "Better response dynamics and Nash equilibrium in discontinuous games," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 68-78.
    7. John Duggan, 2011. "General Conditions for Existence of Maximal Elements via the Uncovered Set," RCER Working Papers 563, University of Rochester - Center for Economic Research (RCER).
    8. Quartieri, Federico, 2022. "A unified view of the existence of maximals," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    9. Salonen, Hannu & Vartiainen, Hannu, 2010. "On the existence of undominated elements of acyclic relations," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 217-221, November.
    10. J. C. R. Alcantud & Carlos Alós-Ferrer, 2002. "Choice-Nash Equilibria," Vienna Economics Papers vie0209, University of Vienna, Department of Economics.
    11. Alcantud, J. C. R. & Manrique, A., 2001. "Continuous representation by a money-metric function," Mathematical Social Sciences, Elsevier, vol. 41(3), pages 365-373, May.
    12. Evren, Özgür & Ok, Efe A., 2011. "On the multi-utility representation of preference relations," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 554-563.
    13. M. Carmen Sánchez & Juan-Vicente Llinares & Begoña Subiza, 2003. "A KKM-result and an application for binary and non-binary choice functions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(1), pages 185-193, January.
    14. Kukushkin, Nikolai S., 2016. "Nash equilibrium with discontinuous utility functions: Reny's approach extended," MPRA Paper 75862, University Library of Munich, Germany.
    15. Nikolai Hoberg & Stefan Baumgärtner, 2014. "Value pluralism, trade-offs and efficiencies," Working Paper Series in Economics 311, University of Lüneburg, Institute of Economics.
    16. Duggan, John, 2011. "General conditions for the existence of maximal elements via the uncovered set," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 755-759.
    17. Hougaard, Jens Leth & Tvede, Mich, 2002. "Benchmark selection: An axiomatic approach," European Journal of Operational Research, Elsevier, vol. 137(1), pages 218-228, February.
    18. Llinares, Juan-Vicente & Sanchez, M. Carmen, 1999. "Non-binary choice functions on non-compact sets," Economics Letters, Elsevier, vol. 63(1), pages 29-32, April.
    19. José Carlos R. Alcantud & Tareq M. Al-shami & A. A. Azzam, 2021. "Caliber and Chain Conditions in Soft Topologies," Mathematics, MDPI, vol. 9(19), pages 1-15, September.
    20. Quartieri, Federico, 2021. "Existence of maximals via right traces," MPRA Paper 107189, University Library of Munich, Germany.

    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:57:y:2009:i:1:p:131-133. 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.