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On the Existence of Undominated Elements of Acyclic Relations

Listed author(s):
  • Hannu Salonen

    (Department of Economics, University of Turku)

  • Hannu Vartiainen

    (The Yrjo Jahnsson Foundation)

We study the existence of undominated elements of acyclic and irreflexive relations. A sufficient condition for the existence is given in the general case without any topological assumptions. Sufficient conditions are also given when the relation in question is defined on a compact Hausdorff space. We study the existence of fixed points of acyclic correspondences, the existence of stable sets, and the possibility of representing the relation by a real valued function.

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File URL: http://econwpa.repec.org/eps/game/papers/0503/0503009.pdf
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Paper provided by EconWPA in its series Game Theory and Information with number 0503009.

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Length: 23 pages
Date of creation: 23 Mar 2005
Handle: RePEc:wpa:wuwpga:0503009
Note: Type of Document - pdf; pages: 23
Contact details of provider: Web page: http://econwpa.repec.org

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  1. Peris, Josep E. & Subiza, Begona, 1995. "A weak utility function for acyclic preferences," Economics Letters, Elsevier, vol. 48(1), pages 21-24, April.
  2. Walker, Mark, 1977. "On the existence of maximal elements," Journal of Economic Theory, Elsevier, vol. 16(2), pages 470-474, December.
  3. Campbell, Donald E. & Walker, Mark, 1990. "Maximal elements of weakly continuous relations," Journal of Economic Theory, Elsevier, vol. 50(2), pages 459-464, April.
  4. J.C. R. Alcantud, 2002. "Characterization of the existence of maximal elements of acyclic relations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(2), pages 407-416.
  5. Peleg, Bezalel, 1970. "Utility Functions for Partially Ordered Topological Spaces," Econometrica, Econometric Society, vol. 38(1), pages 93-96, January.
  6. Josep Enric Peris Ferrando & Begoña Subiza Martínez, 1992. "Maximal elements of non necessarily acyclic binary relations," Working Papers. Serie AD 1992-07, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  7. Bergstrom, Theodore C., 1975. "Maximal elements of acyclic relations on compact sets," Journal of Economic Theory, Elsevier, vol. 10(3), pages 403-404, June.
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