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A utility representation theorem with weaker continuity condition

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  • Inoue, Tomoki

Abstract

We prove that a mixture continuous preference relation has a utility representation if its domain is a convex subset of a finite dimensional vector space. Our condition on the domain of a preference relation is stronger than Eilenberg (1941) and Debreu (1959, 1964), but our condition on the continuity of a preference relation is strictly weaker than the usual continuity assumed by them.

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  • Inoue, Tomoki, 2010. "A utility representation theorem with weaker continuity condition," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 122-127, January.
    • Handle: RePEc:eee:mateco:v:46:y:2010:i:1:p:122-127
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    References listed on IDEAS

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    1. Fishburn, Peter C., 1983. "Transitive measurable utility," Journal of Economic Theory, Elsevier, vol. 31(2), pages 293-317, December.
    2. Toranzo, Margarita Estevez & Beloso, Carlos Herves, 1995. "On the existence of continuous preference orderings without utility representations," Journal of Mathematical Economics, Elsevier, vol. 24(4), pages 305-309.
    3. Monteiro, Paulo Klinger, 1987. "Some results on the existence of utility functions on path connected spaces," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 147-156, April.
    4. Fishburn, P. C., 1983. "Utility functions on ordered convex sets," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 221-232, December.
    5. Inoue, Tomoki, 2011. "A utility representation theorem with weaker continuity condition," Center for Mathematical Economics Working Papers 401, Center for Mathematical Economics, Bielefeld University.
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    Cited by:

    1. Nuh Aygün Dalkıran & Furkan Yıldız, 2021. "Another Characterization of Expected Scott-Suppes Utility Representation," Bogazici Journal, Review of Social, Economic and Administrative Studies, Bogazici University, Department of Economics, vol. 35(2), pages 177-193.
    2. O'Callaghan, Patrick, 2016. "Measuring utility without mixing apples and oranges and eliciting beliefs about stock prices," MPRA Paper 69363, University Library of Munich, Germany.
    3. Uyanik, Metin & Khan, M. Ali, 2022. "The continuity postulate in economic theory: A deconstruction and an integration," Journal of Mathematical Economics, Elsevier, vol. 101(C).

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