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Maximal elements of non necessarily acyclic binary relations


  • Josep Enric Peris Ferrando

    () (Universidad de Alicante)

  • Begoña Subiza Martínez

    () (Universidad de Alicante)


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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  • 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).
  • Handle: RePEc:ivi:wpasad:1992-07

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    References listed on IDEAS

    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. James W. Friedman, 1971. "A Non-cooperative Equilibrium for Supergames," Review of Economic Studies, Oxford University Press, vol. 38(1), pages 1-12.
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    5. Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, vol. 54(3), pages 533-554, May.
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    7. Muthoo, Abhinay, 1992. "Revocable Commitment and Sequential Bargaining," Economic Journal, Royal Economic Society, vol. 102(411), pages 378-387, March.
    8. Asheim, Geir B., 1992. "A unique solution to n-person sequential bargaining," Games and Economic Behavior, Elsevier, vol. 4(2), pages 169-181, April.
    9. Sjostrom, Tomas, 1991. "Stahl's bargaining model," Economics Letters, Elsevier, vol. 36(2), pages 153-157, June.
    10. John Sutton, 1986. "Non-Cooperative Bargaining Theory: An Introduction," Review of Economic Studies, Oxford University Press, vol. 53(5), pages 709-724.
    11. Shaked, Avner & Sutton, John, 1984. "Involuntary Unemployment as a Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 52(6), pages 1351-1364, November.
    12. Yang, Jeong-Ae, 1992. "Another n-person bargaining game with a unique perfect equilibrium," Economics Letters, Elsevier, vol. 38(3), pages 275-277, March.
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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 1-5, 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. 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.
    6. 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.
    7. 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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