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

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Author Info
Andrikopoulos, Athanasios
Zacharias, Eleftherios

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

Find related papers by JEL classification:
D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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  1. BOSSERT, Walter & SPRUMONT, Yves & SUZUMURA, Kotaro, 2002. "Upper Semicontinuous Extensions of Binary Relations," Cahiers de recherche 2002-01, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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  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. [Downloadable!] (restricted)
  3. Duggan, John, 1999. "A General Extension Theorem for Binary Relations," Journal of Economic Theory, Elsevier, vol. 86(1), pages 1-16, May. [Downloadable!] (restricted)
  4. 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!]
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  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. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  7. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December. [Downloadable!] (restricted)
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  8. Subiza, Begona & Peris, Josep E., 1997. "Numerical representation for lower quasi-continuous preferences," Mathematical Social Sciences, Elsevier, vol. 33(2), pages 149-156, April. [Downloadable!] (restricted)
  9. Peris, Josep E. & Subiza, Begona, 1994. "Maximal elements of not necessarily acyclic binary relations," Economics Letters, Elsevier, vol. 44(4), pages 385-388, April. [Downloadable!] (restricted)
  10. 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. [Downloadable!] (restricted)
  11. Donald J. Brown, 1973. "Acyclic Choice," Cowles Foundation Discussion Papers 360, Cowles Foundation, Yale University. [Downloadable!]
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