A KKM-result and an application for binary and non-binary choice functions
By generalizing the classical Knaster-Kuratowski-Mazurkiewicz Theorem, we obtain a result that provides sufficient conditions to ensure the non-emptiness of several kinds of choice functions. This result generalizes well-known results on the existence of maximal elements for binary relations (Bergstrom ; Walker ; Tian ), on the non-emptiness of non-binary choice functions (Nehring ; Llinares and Sánchez ) and on the non-emptiness of some classical solutions for tournaments (top cycle and uncovered set) on non-finite sets. Copyright Springer-Verlag Berlin Heidelberg 2003
Volume (Year): 21 (2003)
Issue (Month): 1 (01)
|Contact details of provider:|| Web page: http://www.springer.com|
|Order Information:||Web: http://www.springer.com/economics/economic+theory/journal/199/PS2|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Juan Vicente Llinares Císcar, 1995. "Unified Treatment Of The Problem Of Existence Of Maximal Elements In Binary Relations. A Characterization," Working Papers. Serie AD 1995-17, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
- Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
- Wayne Shafer & Hugo Sonnenschein, 1974. "Equilibrium in Abstract Economies Without Ordered Preferences," Discussion Papers 94, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Ben-El-Mechaiekh, H. & Chebbi, S. & Florenzano, M. & Llinares, J.-V., 1997. "Abstract Convexity and Fixed Points," Papiers d'Economie MathÃ©matique et Applications 97.87, UniversitÃ© PanthÃ©on-Sorbonne (Paris 1).
- Kim, Taesung & Richter, Marcel K., 1986. "Nontransitive-nontotal consumer theory," Journal of Economic Theory, Elsevier, vol. 38(2), pages 324-363, April.
- 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.
- Nehring, Klaus, 1996. "Maximal elements of non-binary choice functions on compact sets," Economics Letters, Elsevier, vol. 50(3), pages 337-340, March.
- Bergstrom, Theodore C., 1975. "Maximal elements of acyclic relations on compact sets," Journal of Economic Theory, Elsevier, vol. 10(3), pages 403-404, June.
- Klaus Nehring, 1997. "Rational choice and revealed preference without binariness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(3), pages 403-425.
- Moulin, Herve, 1994. "Social choice," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 31, pages 1091-1125 Elsevier.
- Guoqiang Tian, 1993. "Necessary and Sufficient Conditions for Maximization of a Class of Preference Relations," Review of Economic Studies, Oxford University Press, vol. 60(4), pages 949-958.
- Campbell, Donald E. & Walker, Mark, 1990. "Maximal elements of weakly continuous relations," Journal of Economic Theory, Elsevier, vol. 50(2), pages 459-464, April.
- Tian, Guoqiang & Zhou, Jianxin, 1992. "Transfer Method for Characterizing the Existence of Maximal Elements of Binary Relations on Compact or Noncompact Sets," MPRA Paper 41227, University Library of Munich, Germany.
- 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)
When requesting a correction, please mention this item's handle: RePEc:spr:joecth:v:21:y:2003:i:1:p:185-193. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla)or (Rebekah McClure)
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 references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.