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Maximal elements of not necessarily acyclic binary relations

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  • Peris, Josep E.
  • Subiza, Begona

Abstract

The existence of maximal elements for binary preference relations is analyzed without imposing transitivity or convexity conditions. From each preference relation a new acyclic relation is defined in such a way that some maximal elements of this new relation characterize maximal elements of the original one. The result covers the case whereby the relation is acyclic.
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Suggested Citation

  • Peris, Josep E. & Subiza, Begona, 1994. "Maximal elements of not necessarily acyclic binary relations," Economics Letters, Elsevier, vol. 44(4), pages 385-388, April.
    • Handle: RePEc:eee:ecolet:v:44:y:1994:i:4:p:385-388
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    Cited by:

    1. Salonen, Hannu & Vartiainen, Hannu, 2010. "On the existence of undominated elements of acyclic relations," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 217-221, November.
    2. Duggan, John, 2011. "General conditions for the existence of maximal elements via the uncovered set," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 755-759.
    3. Subiza Begoña & Peris Josep E., 2014. "A Solution for General Exchange Markets with Indivisible Goods when Indifferences are Allowed," Mathematical Economics Letters, De Gruyter, vol. 2(3-4), pages 77-81, November.
    4. Peris, Josep E. & Subiza, Begoña, 2013. "A reformulation of von Neumann–Morgenstern stability: m-stability," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 51-55.
    5. Han, Weibin & van Deemen, Adrian, 2021. "The solution of generalized stable sets and its refinement," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 60-67.
    6. Begoña Subiza & Josep Peris, 2005. "Condorcet choice functions and maximal elements," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(3), pages 497-508, June.
    7. Peris, Josep E. & Subiza, Begoña, 2012. "M-stability: A reformulation of Von Neumann-Morgenstern stability," QM&ET Working Papers 12-4, University of Alicante, D. Quantitative Methods and Economic Theory.
    8. Josep E. Peris & Begoña Subiza, 2023. "Rational stability of choice functions," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(3), pages 580-598, September.
    9. Andrikopoulos, Athanasios & Zacharias, Eleftherios, 2008. "General solutions for choice sets: The Generalized Optimal-Choice Axiom set," MPRA Paper 11645, University Library of Munich, Germany.

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