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On the existence of undominated alternatives in convex sets

Author

Listed:
  • Nikolai S. Kukushkin

    () (Dorodnicyn Computing Centre, FRC CSC RAS; Moscow Institute of Physics and Technology, Russia)

Abstract

Necessary and sufficient conditions are found for an interval order to admit a maximizer in every convex, or convex and compact, subset of its domain. The conditions are formulated in terms of "improvement paths" and are somewhat similar to conditions characterizing interval orders admitting a maximizer in every compact subset. For a stronger, "von Neumann-Morgenstern," property - every dominated alternative is dominated by an undominated one - only a sufficient condition is obtained.

Suggested Citation

  • Nikolai S. Kukushkin, 2019. "On the existence of undominated alternatives in convex sets," Economics Bulletin, AccessEcon, vol. 39(3), pages 2129-2136.
  • Handle: RePEc:ebl:ecbull:eb-19-00520
    as

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    File URL: http://www.accessecon.com/Pubs/EB/2019/Volume39/EB-19-V39-I3-P199.pdf
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    References listed on IDEAS

    as
    1. Yannelis, Nicholas C. & Prabhakar, N. D., 1983. "Existence of maximal elements and equilibria in linear topological spaces," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 233-245, December.
    2. Nikolai S. Kukushkin, 2012. "On the Existence of Optima in Complete Chains and Lattices," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 759-767, September.
    3. Mukherji, Anjan, 1977. "The Existence of Choice Functions," Econometrica, Econometric Society, vol. 45(4), pages 889-894, May.
    4. 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.
    5. Smith, Tony E, 1974. "On the Existence of Most-Preferred Alternatives," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 184-194, February.
    6. Campbell, Donald E. & Walker, Mark, 1990. "Maximal elements of weakly continuous relations," Journal of Economic Theory, Elsevier, vol. 50(2), pages 459-464, April.
    7. Kalai, Ehud & Schmeidler, David, 1977. "An admissible set occurring in various bargaining situations," Journal of Economic Theory, Elsevier, vol. 14(2), pages 402-411, April.
    8. Walker, Mark, 1977. "On the existence of maximal elements," Journal of Economic Theory, Elsevier, vol. 16(2), pages 470-474, December.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Preference relation; Interval order; Maximal element; Necessary and sufficient condition;

    JEL classification:

    • D1 - Microeconomics - - Household Behavior
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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