This file is part of IDEAS, which uses RePEc data


[ Papers | Articles | Software | Books | Chapters | Authors | Institutions | JEL Classification | NEP reports | Search | New papers by email | Author registration | Rankings | Volunteers | FAQ | Blog | Help! ]

When Non-transitive Relations Take Maxima and Competitive Equilibria Can't Be Beat

Author info | Abstract | Publisher info | Download info | Related research | Statistics
Author Info
Ted Bergstrom (University of California, Santa Barbara)

Additional information is available for the following registered author(s):

Abstract

The paper generalizes theorems of Ky Fan and Hugo Sonnenschein on the existence of maximal elements for non-transitive relations. I used these results to show that a binary relation could be constructed whose maximal element must be a competitive equilibrium. Thus proving the existence of competitive equilibrium under somewhat more general conditions than had been done previously. In 1975, I thought this was a useful extension of the Gale Mas Collel existence theorem. Journal referees then didn't agree with me, so I let it ripen in my desk for 15 years. I still think it is worth looking at if you are interested in the existence of competitive equilibrium or in maximization of funny preference orderings.

Download Info
To download:

If you experience problems downloading a file, check if you have the proper application to view it first. Information about this may be contained in the File-Format links below. In case of further problems read the IDEAS help file. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://repositories.cdlib.org/cgi/viewcontent.cgi?article=1114&context=ucsbecon
File Format: application/pdf
File Function:
Download Restriction: no

Publisher Info
Paper provided by Department of Economics, UC Santa Barbara in its series University of California at Santa Barbara, Economics Working Paper Series with number 1992A.

Download reference. The following formats are available: HTML, plain text, BibTeX, RIS (EndNote), ReDIF
Length:
Date of creation: 01 Jul 2003
Date of revision:
Handle: RePEc:cdl:ucsbec:1992a

Note: oai:cdlib1:
Contact details of provider:
Postal: 2127 North Hall, Santa Barbara, CA 93106-9210
Phone: (805) 893-3670
Fax: (805) 893-8830
Web page: http://repositories.cdlib.org/ucsbecon/dwp/
More information through EDIRC

For technical questions regarding this item, or to correct its listing, contact: (Christopher F. Baum).

Related research
Keywords: existence of competitive equilibrium non-transitive consumers maximal elements Arrow-Debreu model

Other versions of this item:

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.:
  1. Yannelis, Nicholas C. & Prabhakar, N. D., 1983. "Existence of maximal elements and equilibria in linear topological spaces," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 233-245, December. [Downloadable!] (restricted)
  2. Ted Bergstrom, 1975. "Maximal elements of Acyclic Relations on Compact Sets," University of California at Santa Barbara, Economics Working Paper Series 1975B, Department of Economics, UC Santa Barbara. [Downloadable!]
    Other versions:
  3. Mehta, Ghanshyam, 1987. "Weakly lower demicontinuous preference maps," Economics Letters, Elsevier, vol. 23(1), pages 15-18. [Downloadable!] (restricted)
  4. Schofield, Norman., . "Existence of Equilibrium on a Manifold," Working Papers 482, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
  5. Schofield, Norman., . "Social Equilibrium and Cycles on Compact Sets," Working Papers 484, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
    Other versions:
  6. Geistdoerfer-Florenzano, Monique, 1982. "The gale-nikaido-debreu lemma and the existence of transitive equilibrium with or without the free-disposal assumption," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 113-134, January. [Downloadable!] (restricted)
  7. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December. [Downloadable!] (restricted)
  8. Shafer, Wayne J., 1976. "Equilibrium in economies without ordered preferences or free disposal," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 135-137, July. [Downloadable!] (restricted)
  9. Birchenhall, C. R., 1977. "Conditions for the existence of maximal elements in compact sets," Journal of Economic Theory, Elsevier, vol. 16(1), pages 111-115, October. [Downloadable!] (restricted)
  10. McKenzie, Lionel W, 1981. "The Classical Theorem on Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 49(4), pages 819-41, June. [Downloadable!] (restricted)
  11. Shafer, Wayne J, 1974. "The Nontransitive Consumer," Econometrica, Econometric Society, vol. 42(5), pages 913-19, September. [Downloadable!] (restricted)
  12. Ted Bergstrom & Robert Parks & Trout Rader, 1976. "Preferences Which Have Open Graphs," University of California at Santa Barbara, Economics Working Paper Series 1976B, Department of Economics, UC Santa Barbara. [Downloadable!]
    Other versions:
  13. Aliprantis, Charalambos D. & Brown, Donald J., 1983. "Equilibria in markets with a Riesz space of commodities," Journal of Mathematical Economics, Elsevier, vol. 11(2), pages 189-207, April. [Downloadable!] (restricted)
    Other versions:
  14. Ted Bergstrom, 1975. "The Existence of Maximal Elements and Equilibria in the Absence of Transitivity," University of California at Santa Barbara, Economics Working Paper Series 1975C, Department of Economics, UC Santa Barbara. [Downloadable!]
  15. Walker, Mark, 1977. "On the existence of maximal elements," Journal of Economic Theory, Elsevier, vol. 16(2), pages 470-474, December. [Downloadable!] (restricted)
  16. Shafer, Wayne & Sonnenschein, Hugo, 1976. "Equilibrium with Externalities, Commodity Taxation, and Lump Sum Transfers," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(3), pages 601-11, October. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, 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.)

  1. Norman Schofield & Robert P. Parks, 1993. "EXISTENCE OF NASH EQUILIBRIUM IN A SPATIAL MODEL OF n-PARTY COMPETITION," Public Economics 9308002, EconWPA, revised 25 Aug 1993. [Downloadable!]
Statistics
Access and download statistics

Did you know? Over 77% of the top 1000 economists are registered on RePEc.

This page was last updated on 2008-9-30.

This information is provided to you by IDEAS at the Department of Economics, College of Liberal Arts and Sciences, University of Connecticut using RePEc data on a server sponsored by the Society for Economic Dynamics.