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Subextremal functions and lattice programming


  • Marco LiCalzi

    (University of Venice, Italy)

  • Arthur F. Veinott

    (Stanford University)


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, EconWPA.
  • Handle: RePEc:wpa:wuwpge:0509001
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    Cited by:

    1. 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.
    2. Manjira Datta & Kevin L. Reffett, 2005. "Isotone Recursive Methods: the Case of Homogeneous Agents," Tinbergen Institute Discussion Papers 05-012/2, Tinbergen Institute.
    3. Kukushkin, Nikolai S., 2017. "Better response dynamics and Nash equilibrium in discontinuous games," MPRA Paper 81460, University Library of Munich, Germany.
    4. 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.
    5. Anne-Christine Barthel & Tarun Sabarwal, 2016. "Directional Monotone Comparative Statics," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201601, University of Kansas, Department of Economics.
    6. Kukushkin, Nikolai S., 2016. "Nash equilibrium with discontinuous utility functions: Reny's approach extended," MPRA Paper 75862, University Library of Munich, Germany.
    7. 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.
    8. 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.
    9. Koji Shirai, 2008. "A generalization of monotone comparative statics," Economics Bulletin, AccessEcon, vol. 3(39), pages 1-9.
    10. 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.
    11. Kukushkin, Nikolai S., 2015. "Cournot tatonnement in aggregative games with monotone best responses," MPRA Paper 66976, University Library of Munich, Germany.
    12. 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.

    More about this item


    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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