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On the Existence of Optima in Complete Chains and Lattices

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  • Nikolai S. Kukushkin

    (Russian Academy of Sciences)

Abstract

A necessary and sufficient condition for a preference ordering defined on a chain-complete poset to attain its maximum in every subcomplete chain is obtained. A meet-superextremal, or join-superextremal, function on a complete lattice attains its maximum in every subcomplete sublattice if and only if it attains a maximum in every subcomplete chain.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:154:y:2012:i:3:d:10.1007_s10957-012-0031-8
    DOI: 10.1007/s10957-012-0031-8
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    References listed on IDEAS

    as
    1. Nikolai Kukushkin, 2013. "Monotone comparative statics: changes in preferences versus changes in the feasible set," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(3), pages 1039-1060, April.
    2. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    3. 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.
    4. Nikolai S Kukushkin, 2005. "On the existence of maximal elements: An impossibility theorem," Game Theory and Information 0509004, University Library of Munich, Germany.
    5. Marco LiCalzi & Arthur F. Veinott, 2005. "Subextremal functions and lattice programming," GE, Growth, Math methods 0509001, University Library of Munich, Germany.
    6. Kukushkin, Nikolai S., 2011. "Monotone comparative statics: Changes in preferences vs changes in the feasible set," MPRA Paper 31612, University Library of Munich, Germany.
    7. Kukushkin, Nikolai S., 2008. "Maximizing an interval order on compact subsets of its domain," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 195-206, September.
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    Cited by:

    1. Kukushkin, Nikolai S., 2023. "Maximizing a preference relation on complete chains and lattices," MPRA Paper 119148, University Library of Munich, Germany.
    2. Nikolai S. Kukushkin, 2019. "On the existence of undominated alternatives in convex sets," Economics Bulletin, AccessEcon, vol. 39(3), pages 2129-2136.
    3. Lu Yu, 2024. "Nash equilibria of quasisupermodular games," Papers 2406.13783, arXiv.org.

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