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Numerical representation for lower quasi-continuous preferences

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  • Subiza, Begona
  • Peris, Josep E.

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.
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  • Subiza, Begona & Peris, Josep E., 1997. "Numerical representation for lower quasi-continuous preferences," Mathematical Social Sciences, Elsevier, vol. 33(2), pages 149-156, April.
    • Handle: RePEc:eee:matsoc:v:33:y:1997:i:2:p:149-156
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    References listed on IDEAS

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    1. Campbell, Donald E. & Walker, Mark, 1990. "Maximal elements of weakly continuous relations," Journal of Economic Theory, Elsevier, vol. 50(2), pages 459-464, April.
    2. Trout Rader, 1963. "The Existence of a Utility Function to Represent Preferences," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(3), pages 229-232.
    3. Bergstrom, Theodore C., 1975. "Maximal elements of acyclic relations on compact sets," Journal of Economic Theory, Elsevier, vol. 10(3), pages 403-404, June.
    4. Walker, Mark, 1977. "On the existence of maximal elements," Journal of Economic Theory, Elsevier, vol. 16(2), pages 470-474, December.
    5. Tian, Guoqiang & Zhou, Jianxin, 1995. "Transfer continuities, generalizations of the Weierstrass and maximum theorems: A full characterization," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 281-303.
    6. Peleg, Bezalel, 1970. "Utility Functions for Partially Ordered Topological Spaces," Econometrica, Econometric Society, vol. 38(1), pages 93-96, January.
    7. Peris, Josep E. & Subiza, Begona, 1995. "A weak utility function for acyclic preferences," Economics Letters, Elsevier, vol. 48(1), pages 21-24, April.
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    Cited by:

    1. 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.
    2. Bosi, Gianni & Zuanon, Magalì, 2014. "Upper semicontinuous representations of interval orders," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 60-63.
    3. Gorno, Leandro & Rivello, Alessandro T., 2023. "A maximum theorem for incomplete preferences," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    4. Rodriguez-Palmero, Carlos, 1997. "A representation of acyclic preferences," Economics Letters, Elsevier, vol. 54(2), pages 143-146, February.
    5. Quartieri, Federico, 2022. "A unified view of the existence of maximals," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    6. 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.
    7. Quartieri, Federico, 2021. "Existence of maximals via right traces," MPRA Paper 107189, University Library of Munich, Germany.
    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. 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.
    10. 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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