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General solutions for choice sets: The Generalized Optimal-Choice Axiom set

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  • Andrikopoulos, Athanasios
  • Zacharias, Eleftherios

Abstract

In this paper we characterize the existence of best choices of arbitrary binary relations over non finite sets of alternatives, according to the Generalized Optimal-Choice Axiom condition introduced by Schwartz. We focus not just in the best choices of a single set X, but rather in the best choices of all the members of a family K of subsets of X. Finally we generalize earlier known results concerning the existence (or the characterization) of maximal elements of binary relations on compact subsets of a given space of alternatives.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 11645.

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Date of creation: 2008
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Handle: RePEc:pra:mprapa:11645

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Keywords: Generalized Optimal-Choice Axiom; maximal elements; acyclicity; consistency; ≻-upper compactness;

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  1. Donald J. Brown, 1973. "Acyclic Choice," Cowles Foundation Discussion Papers 360, Cowles Foundation for Research in Economics, Yale University.
  2. Josep Enric Peris Ferrando & Begoña Subiza Martínez, 1996. "Numerical representation for lower quasi-continuous preferences," Working Papers. Serie AD 1996-08, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  3. Bossert, Walter & Sprumont, Yves & Suzumura, Kotaro, 2002. "Upper semicontinuous extensions of binary relations," Journal of Mathematical Economics, Elsevier, vol. 37(3), pages 231-246, May.
  4. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
  5. Borglin, Anders & Keiding, Hans, 1976. "Existence of equilibrium actions and of equilibrium : A note on the `new' existence theorems," Journal of Mathematical Economics, Elsevier, vol. 3(3), pages 313-316, December.
  6. Yannelis, Nicholas C., 1985. "Maximal elements over non-compact subsets of linear topological spaces," Economics Letters, Elsevier, vol. 17(1-2), pages 133-136.
  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.
  8. Duggan, John, 1999. "A General Extension Theorem for Binary Relations," Journal of Economic Theory, Elsevier, vol. 86(1), pages 1-16, May.
  9. J.C. R. Alcantud, 2002. "Characterization of the existence of maximal elements of acyclic relations," Economic Theory, Springer, vol. 19(2), pages 407-416.
  10. 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.
  11. Suzumura, Kataro, 1976. "Remarks on the Theory of Collective Choice," Economica, London School of Economics and Political Science, vol. 43(172), pages 381-90, November.
  12. 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).
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