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On the characterization of preference continuity by chains of sets

Author

Listed:
  • Carlos Alós-Ferrer

    (University of Cologne)

  • Klaus Ritzberger

    (Institute for Advanced Studies Vienna, and Vienna Graduate School of Finance)

Abstract

This paper characterizes continuity and upper and lower semicontinuity of preference relations, which may or may not be representable by utility functions, on arbitrary topological spaces. One characterization is by the existence of an appropriate chain of sets. This approach can be used to generate preference relations that fulfill predetermined conditions, to obtain examples or counterexamples. The second characterization of continuity is closely related to the concept of scale, but, in contrast to previous work, does not rely on the existence of a utility function.

Suggested Citation

  • Carlos Alós-Ferrer & Klaus Ritzberger, 2015. "On the characterization of preference continuity by chains of sets," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 115-128, October.
    • Handle: RePEc:spr:etbull:v:3:y:2015:i:2:d:10.1007_s40505-014-0048-2
    DOI: 10.1007/s40505-014-0048-2
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    References listed on IDEAS

    as
    1. Herden, G., 1989. "On the existence of utility functions," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 297-313, June.
    2. Athanasios Andrikopoulos, 2013. "Compactness in the choice and game theories: a characterization of rationality," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(2), pages 105-110, November.
    3. Herden, G., 1989. "On the existence of utility functions ii," Mathematical Social Sciences, Elsevier, vol. 18(2), pages 107-117, October.
    4. J. Alcantud & G. Bosi & M. Campión & J. Candeal & E. Induráin & C. Rodríguez-Palmero, 2008. "Continuous Utility Functions Through Scales," Theory and Decision, Springer, vol. 64(4), pages 479-494, June.
    5. Bosi, G. & Mehta, G. B., 2002. "Existence of a semicontinuous or continuous utility function: a unified approach and an elementary proof," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 311-328, November.
    6. 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.
    7. 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.
    8. Bergstrom, Theodore C., 1975. "Maximal elements of acyclic relations on compact sets," Journal of Economic Theory, Elsevier, vol. 10(3), pages 403-404, June.
    9. Walker, Mark, 1977. "On the existence of maximal elements," Journal of Economic Theory, Elsevier, vol. 16(2), pages 470-474, December.
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    More about this item

    Keywords

    Preferences; Continuity;

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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