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Existence of a convex extension of a preference relation

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  • Paolo Scapparone

Abstract

In questo lavoro diciamo che una relazione di preferenza (ossia irriflessiva)P èregolare (o unordinamento debole) se tanto essa quanto la sua relazione di non paragonabilità sono transitive; diciamo anche che una relazione di preferenzaP * costituisce un'estensione convessa di un'altra relazione di preferenzaP se vale l'inclusioneP⊆P * eP * è regolare ed a valori convessi. Provereino che un'estensione convessa dellaP esiste se e solo se ogni insieme non vuoto e finito di alternativeA non è incluso nell'involucro convesso dell'insieme ∪ x∈A P(x). Copyright Associazione per la Matematica Applicata alle Scienze Economiche e Sociali (AMASES) 1999

Suggested Citation

  • Paolo Scapparone, 1999. "Existence of a convex extension of a preference relation," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 22(1), pages 5-11, March.
    • Handle: RePEc:spr:decfin:v:22:y:1999:i:1:p:5-11
    DOI: 10.1007/BF02912347
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    References listed on IDEAS

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    1. Levin, V. L., 1991. "Some applications of set-valued mappings in mathematical economics," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 69-87.
    2. Sondermann, Dieter, 1980. "Utility representations for partial orders," Journal of Economic Theory, Elsevier, vol. 23(2), pages 183-188, October.
    3. Peleg, Bezalel, 1970. "Utility Functions for Partially Ordered Topological Spaces," Econometrica, Econometric Society, vol. 38(1), pages 93-96, January.
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    Cited by:

    1. Demuynck, Thomas, 2009. "A general extension result with applications to convexity, homotheticity and monotonicity," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 96-109, January.
    2. Scapparone, Paolo, 2015. "Existence of an upper hemi-continuous and convex-valued demand sub-correspondence," Mathematical Social Sciences, Elsevier, vol. 75(C), pages 123-129.
    3. Athanasios Andrikopoulos, 2019. "On the extension of binary relations in economic and game theories," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 277-285, June.
    4. T. Demuynck, 2009. "Common ordering extensions," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 09/593, Ghent University, Faculty of Economics and Business Administration.

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    More about this item

    Keywords

    Preference relations; Convexity; 90A06; JEL classification: D11;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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