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On the existence of maximal elements: An impossibility theorem

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Author Info
Nikolai S Kukushkin (Russian Academy of Sciences Dorodnicyn Computing Center)

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Abstract

Most properties of binary relations considered in the decision literature can be expressed as the impossibility of certain ``configurations.'' There exists no condition of this form which would hold for a binary relation on a subset of a finite-dimensional Euclidean space if and only if the relation admits a maximal element on every nonempty compact subset of its domain.

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File URL: http://129.3.20.41/eps/game/papers/0509/0509004.pdf
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Publisher Info
Paper provided by EconWPA in its series Game Theory and Information with number 0509004.

Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Length: 7 pages
Date of creation: 28 Sep 2005
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Handle: RePEc:wpa:wuwpga:0509004

Note: Type of Document - pdf; pages: 7
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Web page: http://129.3.20.41

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Related research
Keywords: Binary relation; Maximal element; Necessary and sufficient condition; Potential games;

Find related papers by JEL classification:
D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

This paper has been announced in the following NEP Reports:

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. 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:
  2. Mukherji, Anjan, 1977. "The Existence of Choice Functions," Econometrica, Econometric Society, vol. 45(4), pages 889-94, May. [Downloadable!] (restricted)
  3. Smith, Tony E, 1974. "On the Existence of Most-Preferred Alternatives," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 184-94, February. [Downloadable!] (restricted)
  4. Campbell, Donald E. & Walker, Mark, 1990. "Maximal elements of weakly continuous relations," Journal of Economic Theory, Elsevier, vol. 50(2), pages 459-464, April. [Downloadable!] (restricted)
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This page was last updated on 2009-12-2.

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