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The existence of maximal elements: generalized lexicographic relations

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  • Hougaard, Jens Leth
  • Tvede, Mich

Abstract

In the present paper, the existence of maximal elements for binary relations are studied. Generalized lexicographic relations are introduced, and some results on existence of maximal elements are provided. A simple example shows that economies with "lexicographic consumers" need not have equilibria even though demand functions associated with generalized lexicographic relations may be continuous for positive prices.

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Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 36 (2001)
Issue (Month): 2 (November)
Pages: 111-115

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Handle: RePEc:eee:mateco:v:36:y:2001:i:2:p:111-115

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  1. Knoblauch, Vicki, 2000. "Lexicographic orders and preference representation," Journal of Mathematical Economics, Elsevier, vol. 34(2), pages 255-267, October.
  2. 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.
  3. Walker, Mark, 1977. "On the existence of maximal elements," Journal of Economic Theory, Elsevier, vol. 16(2), pages 470-474, December.
  4. Bergstrom, Theodore C., 1975. "Maximal elements of acyclic relations on compact sets," Journal of Economic Theory, Elsevier, vol. 10(3), pages 403-404, June.
  5. 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).
  6. Michael Lockwood, 1999. "Preference Structures, Property Rights, and Paired Comparisons," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 13(1), pages 107-122, January.
  7. Colman, Andrew M. & Stirk, Jonathan A., 1999. "Singleton bias and lexicographic preferences among equally valued alternatives," Journal of Economic Behavior & Organization, Elsevier, vol. 40(4), pages 337-351, December.
  8. Fishburn, Peter C, 1975. "Axioms for Lexicographic Preferences," Review of Economic Studies, Wiley Blackwell, vol. 42(3), pages 415-19, July.
  9. Tian, Guoqiang, 1993. "Necessary and Sufficient Conditions for Maximization of a Class of Preference Relations," Review of Economic Studies, Wiley Blackwell, vol. 60(4), pages 949-58, October.
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Cited by:
  1. Vicki Knoblauch, 2003. "Continuous Lexicographic Preferences," Working papers 2003-31, University of Connecticut, Department of Economics.

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