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Monotone comparative statics on semilattices

Author

Listed:
  • Nikolai S. Kukushkin

    (Dorodnicyn Computing Centre, FRC CSC RAS)

Abstract

This paper examines to what extent monotone comparative statics analysis in the style of Milgrom and Shannon (1994) can be extended from lattices to semilattices (e.g., budget sets). A condition on preference orderings is found which is necessary and sufficient for a monotone response of the optimal choice from every subsemilattice to a perturbation of the preferences satisfying an appropriate single crossing condition. A strategic game model related to the consumption of positional goods is formulated where Nash equilibrium exists because the players' preferences satisfy our condition.

Suggested Citation

  • Nikolai S. Kukushkin, 2021. "Monotone comparative statics on semilattices," Economics Bulletin, AccessEcon, vol. 41(3), pages 1711-1718.
    • Handle: RePEc:ebl:ecbull:eb-21-00194
    as

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    File URL: http://www.accessecon.com/Pubs/EB/2021/Volume41/EB-21-V41-I3-P146.pdf
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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. Tobias Harks & Max Klimm & Rolf Möhring, 2013. "Strong equilibria in games with the lexicographical improvement property," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 461-482, May.
    4. Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 209-227, March.
    5. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    6. John K.-H Quah, 2007. "The Comparative Statics of Constrained Optimization Problems," Econometrica, Econometric Society, vol. 75(2), pages 401-431, March.
    7. Kukushkin, Nikolai S., 2017. "Strong Nash equilibrium in games with common and complementary local utilities," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 1-12.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Semilattice; Monotone comparative statics; Single crossing; Strategic complementarities; Nash equilibrium;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D1 - Microeconomics - - Household Behavior

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