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Unified Treatment Of The Problem Of Existence Of Maximal Elements In Binary Relations. A Characterization

Author

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  • Juan Vicente Llinares Císcar

    (Universidad de Murcia)

Abstract

The aim of this paper is twofold. On the one hand to present by means of a unique statement an existence result which covers both ways (convexity and acyclicity) of analyzing the problem of existence of maximal elements of non transitive binary relations. And on the other hand, to introduce the concept of an abstract convexity structure, which we call mc-spaces, that generalizes the notion of usual convexity. It is presented as a powerful tool which allows many problems which have only been analyzed (previously) under convexity conditions to be solved.

Suggested Citation

  • Juan Vicente Llinares Císcar, 1995. "Unified Treatment Of The Problem Of Existence Of Maximal Elements In Binary Relations. A Characterization," Working Papers. Serie AD 1995-17, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    • Handle: RePEc:ivi:wpasad:1995-17
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    File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-1995-17.pdf
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    Cited by:

    1. Llinarès, Juan Vicente, 1998. "Existence of equilibrium in generalized games with non-convex strategy spaces," CEPREMAP Working Papers (Couverture Orange) 9801, CEPREMAP.
    2. Llinarès, Juan Vicente, 1998. "Abstract convexity, some relations and applications," CEPREMAP Working Papers (Couverture Orange) 9803, CEPREMAP.
    3. Hougaard, Jens Leth & Tvede, Mich, 2001. "The existence of maximal elements: generalized lexicographic relations," Journal of Mathematical Economics, Elsevier, vol. 36(2), pages 111-115, November.
    4. Florian Brandl & Felix Brandt, 2020. "Arrovian Aggregation of Convex Preferences," Econometrica, Econometric Society, vol. 88(2), pages 799-844, March.
    5. Alcantud, J.C.R., 2008. "Mixed choice structures, with applications to binary and non-binary optimization," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 242-250, February.
    6. Francesco Ciardiello, 2007. "Convexity on Nash Equilibria without Linear Structure," Quaderni DSEMS 15-2007, Dipartimento di Scienze Economiche, Matematiche e Statistiche, Universita' di Foggia.
    7. M. Carmen Sánchez & Juan-Vicente Llinares & Begoña Subiza, 2003. "A KKM-result and an application for binary and non-binary choice functions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(1), pages 185-193, January.
    8. J. V. Llinares, 2000. "Existence of Equilibrium in Generalized Games with Abstract Convexity Structure," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 149-160, April.

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