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Maximizing an interval order on compact subsets of its domain

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  • Kukushkin, Nikolai S.

Abstract

Maximal elements of a binary relation on compact subsets of a metric space define a choice function. An infinite extension of transitivity is necessary and sufficient for such a choice function to be nonempty-valued and path independent (or satisfy the outcast axiom). An infinite extension of acyclicity is necessary and sufficient for the choice function to have nonempty values provided the underlying relation is an interval order.

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Bibliographic Info

Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 56 (2008)
Issue (Month): 2 (September)
Pages: 195-206

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Handle: RePEc:eee:matsoc:v:56:y:2008:i:2:p:195-206

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Web page: http://www.elsevier.com/locate/inca/505565

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Keywords: Maximal element Path independence Outcast axiom Interval order Semiorder;

References

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  1. Walker, Mark, 1977. "On the existence of maximal elements," Journal of Economic Theory, Elsevier, vol. 16(2), pages 470-474, December.
  2. Kukushkin, Nikolai S., 2006. "On the choice of most-preferred alternatives," MPRA Paper 803, University Library of Munich, Germany.
  3. Bergstrom, Theodore C., 1975. "Maximal elements of acyclic relations on compact sets," Journal of Economic Theory, Elsevier, vol. 10(3), pages 403-404, June.
  4. Nikolai S Kukushkin, 2005. "On the existence of maximal elements: An impossibility theorem," Game Theory and Information, EconWPA 0509004, EconWPA.
  5. Alcantud, Jose C.R., 2006. "Maximality with or without binariness: Transfer-type characterizations," Mathematical Social Sciences, Elsevier, Elsevier, vol. 51(2), pages 182-191, March.
  6. Kukushkin, Nikolai S., 1999. "Potential games: a purely ordinal approach," Economics Letters, Elsevier, vol. 64(3), pages 279-283, September.
  7. Campbell, Donald E. & Walker, Mark, 1990. "Maximal elements of weakly continuous relations," Journal of Economic Theory, Elsevier, vol. 50(2), pages 459-464, April.
  8. Mukherji, Anjan, 1977. "The Existence of Choice Functions," Econometrica, Econometric Society, Econometric Society, vol. 45(4), pages 889-94, May.
  9. Nehring, Klaus, 1996. "Maximal elements of non-binary choice functions on compact sets," Economics Letters, Elsevier, vol. 50(3), pages 337-340, March.
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Cited by:
  1. Kukushkin, Nikolai S., 2014. "Strong equilibrium in games with common and complementary local utilities," MPRA Paper 55499, University Library of Munich, Germany.
  2. Kukushkin, Nikolai S., 2010. "On the existence of most-preferred alternatives in complete lattices," MPRA Paper 27504, University Library of Munich, Germany.
  3. Kukushkin, Nikolai S., 2012. "Cournot tatonnement and potentials," MPRA Paper 43188, University Library of Munich, Germany.

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