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Upper Semicontinuous Representability of Maximal Elements for Nontransitive Preferences

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  • Gianni Bosi

    (University of Trieste)

  • Magalì Zuanon

    (University of Brescia)

Abstract

We characterize the possibility of determining all the maximal elements for a preorder on a topological space by maximizing all the functions in a suitable family of upper semicontinuous order-preserving functions. We discuss the possibility of extending this result to the case of a quasi-preorder (i.e., a reflexive and Suzumura consistent binary relation) on a topological space.

Suggested Citation

  • Gianni Bosi & Magalì Zuanon, 2019. "Upper Semicontinuous Representability of Maximal Elements for Nontransitive Preferences," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 758-765, June.
    • Handle: RePEc:spr:joptap:v:181:y:2019:i:3:d:10.1007_s10957-019-01495-x
    DOI: 10.1007/s10957-019-01495-x
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    References listed on IDEAS

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    1. White, D. J., 1980. "Optimality and efficiency I," European Journal of Operational Research, Elsevier, vol. 4(5), pages 346-355, May.
    2. 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.
    3. Susumu Cato, 2012. "Szpilrajn, Arrow And Suzumura: Concise Proofs Of Extension Theorems And An Extension," Metroeconomica, Wiley Blackwell, vol. 63(2), pages 235-249, May.
    4. White, D. J., 1980. "Notes in decision theory: Optimality and efficiency II," European Journal of Operational Research, Elsevier, vol. 4(6), pages 426-427, June.
    5. Peleg, Bezalel, 1970. "Utility Functions for Partially Ordered Topological Spaces," Econometrica, Econometric Society, vol. 38(1), pages 93-96, January.
    6. Gianni Bosi & Magalì E. Zuanon, 2017. "Maximal elements of quasi upper semicontinuous preorders on compact spaces," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 109-117, April.
    7. Podinovski, Vladislav V., 2013. "Non-dominance and potential optimality for partial preference relations," European Journal of Operational Research, Elsevier, vol. 229(2), pages 482-486.
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    Cited by:

    1. Quartieri, Federico, 2022. "A unified view of the existence of maximals," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    2. Quartieri, Federico, 2021. "Existence of maximals via right traces," MPRA Paper 107189, University Library of Munich, Germany.

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