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Numerical representation for lower quasi-continuous preferences

Author

Listed:
  • Josep Enric Peris Ferrando

    (Universidad de Alicante)

  • Begoña Subiza Martínez

    (Universidad de Alicante)

Abstract

A weaker than usual continuity condition for acyclic preferences is introduced. For preorders this condition turns out to be equivalent to lower continuity, but in general this is not true. By using this condition, a numerical representation which is upper semicontinuous is obtained. This fact guarantees the existence of maxima of such a function, and therefore the existence of maximal elements of the binary relation.

Suggested Citation

  • 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).
    • Handle: RePEc:ivi:wpasad:1996-08
    as

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    File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-1996-08.pdf
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    Cited by:

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    2. Athanasios Andrikopoulos, 2016. "A characterization of the generalized optimal choice set through the optimization of generalized weak utilities," Theory and Decision, Springer, vol. 80(4), pages 611-621, April.
    3. Quartieri, Federico, 2022. "A unified view of the existence of maximals," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    4. Bosi, Gianni & Sbaiz, Gabriele, 2025. "Upper semicontinuous utilities for all upper semicontinuous total preorders," Mathematical Social Sciences, Elsevier, vol. 134(C), pages 31-41.
    5. Athanasios Andrikopoulos, 2011. "Characterization of the existence of semicontinuous weak utilities for binary relations," Theory and Decision, Springer, vol. 70(1), pages 13-26, January.
    6. Quartieri, Federico, 2021. "Existence of maximals via right traces," MPRA Paper 107189, University Library of Munich, Germany.
    7. Bosi, Gianni & Zuanon, Magalì, 2014. "Upper semicontinuous representations of interval orders," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 60-63.
    8. Alcantud, J. C. R. & Rodriguez-Palmero, C., 1999. "Characterization of the existence of semicontinuous weak utilities," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 503-509, December.
    9. Gorno, Leandro & Rivello, Alessandro T., 2023. "A maximum theorem for incomplete preferences," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    10. Rodriguez-Palmero, Carlos, 1997. "A representation of acyclic preferences," Economics Letters, Elsevier, vol. 54(2), pages 143-146, February.
    11. Rodriguez-Palmero, Carlos & Garcia-Lapresta, Jose-Luis, 2002. "Maximal elements for irreflexive binary relations on compact sets," Mathematical Social Sciences, Elsevier, vol. 43(1), pages 55-60, January.
    12. 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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