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Subextremal functions and lattice programming

Author

Listed:
  • Marco LiCalzi

    (University of Venice, Italy)

  • Arthur F. Veinott

    (Stanford University)

Abstract

Let M and N be the set of minimizers of a function f over respective subsets K and L of a lattice, with K being lower than L. This paper characterizes the class of functions f for which M is lower (resp., weakly lower, meet lower, join lower, chain lower) than N for all K lower than L. The resulting five classes of functions, called subextremal variants, have alternate characterizations by variants of the downcrossing-differences property, i.e., their first differences change sign at most once from plus to minus along complementary chains.

Suggested Citation

  • Marco LiCalzi & Arthur F. Veinott, 2005. "Subextremal functions and lattice programming," GE, Growth, Math methods 0509001, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpge:0509001
    Note: Type of Document - pdf; pages: 21. 21 pages, scanned from original on paper to a PDF
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/ge/papers/0509/0509001.pdf
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    Citations

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    Cited by:

    1. Manjira Datta & Kevin L. Reffett, 2005. "Isotone Recursive Methods: the Case of Homogeneous Agents," Tinbergen Institute Discussion Papers 05-012/2, Tinbergen Institute.
    2. Manjira Datta & Leonard Mirman & Olivier Morand & Kevin Reffett, 2002. "Monotone Methods for Markovian Equilibrium in Dynamic Economies," Annals of Operations Research, Springer, vol. 114(1), pages 117-144, August.
    3. Nikolai S. Kukushkin, 2016. "Cournot Tatonnement in Aggregative Games with Monotone Best Responses," Springer Series in Game Theory, in: Pierre von Mouche & Federico Quartieri (ed.), Equilibrium Theory for Cournot Oligopolies and Related Games, pages 31-45, Springer.
    4. Anne-Christine Barthel & Tarun Sabarwal, 2018. "Directional monotone comparative statics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 557-591, October.
    5. Łukasz Balbus & Paweł Dziewulski & Kevin Reffett & Łukasz Woźny, 2015. "Differential information in large games with strategic complementarities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 201-243, May.
    6. 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.
    7. Koji Shirai, 2008. "A generalization of monotone comparative statics," Economics Bulletin, AccessEcon, vol. 3(39), pages 1-9.
    8. 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.
    9. Mirman, Leonard J. & Morand, Olivier F. & Reffett, Kevin L., 2008. "A qualitative approach to Markovian equilibrium in infinite horizon economies with capital," Journal of Economic Theory, Elsevier, vol. 139(1), pages 75-98, March.
    10. Elena Antoniadou & Leonard J Mirman & Richard Ruble, 2014. "Lattices and Lotteries," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 445-463, May.
    11. Kukushkin, Nikolai S., 2018. "Better response dynamics and Nash equilibrium in discontinuous games," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 68-78.
    12. Elena Antoniadou, 2007. "Comparative Statics for the Consumer Problem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(1), pages 189-203, April.
    13. Kukushkin, Nikolai S., 2016. "Nash equilibrium with discontinuous utility functions: Reny's approach extended," MPRA Paper 75862, University Library of Munich, Germany.
    14. Leonard J. Mirman & Richard Ruble, 2008. "Lattice Theory and the Consumer's Problem," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 301-314, May.
    15. Sobel, Joel, 2019. "Iterated weak dominance and interval-dominance supermodular games," Theoretical Economics, Econometric Society, vol. 14(1), January.
    16. Manjira Datta & Leonard Mirman & Kevin Reffett, "undated". "Nonclassical Brock-Mirman Economies," Working Papers 2179544, Department of Economics, W. P. Carey School of Business, Arizona State University.
    17. Bar Light, 2019. "Stochastic Comparative Statics in Markov Decision Processes," Papers 1904.05481, arXiv.org, revised Jan 2020.

    More about this item

    Keywords

    Comparative statics; supermodular functions;

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D9 - Microeconomics - - Micro-Based Behavioral Economics

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