IDEAS home Printed from https://ideas.repec.org/a/ebl/ecbull/eb-08c00009.html
   My bibliography  Save this article

A generalization of monotone comparative statics

Author

Listed:
  • Koji Shirai

    (Waseda University, Graduate School of Economics)

Abstract

In this paper, we generalize the lattice theoretical comparative statics by Li Calzi and Veinott, and Milgrom and Shannon. While their theorem is constructed on lattices, particularly on partially ordered sets, we do not require the antisymmetry on a binary relation defined on the set. On the basis of this result, we can deal with the comparative statics of constrained optimization problems, including the cases with nonlinear constraints, in a very intuitive, but considerably general fashion. Specifically, we can extend the "value order methods" proposed by Antoniadou and Mirman and Ruble in the context of consumer problems with linear constraints. It is also worth noting that our results on the value order can be applicable for any comparative criterion as long as it is a complete preorder on the domain of the objective function.

Suggested Citation

  • Koji Shirai, 2008. "A generalization of monotone comparative statics," Economics Bulletin, AccessEcon, vol. 3(39), pages 1-9.
    • Handle: RePEc:ebl:ecbull:eb-08c00009
    as

    Download full text from publisher

    File URL: http://www.accessecon.com/pubs/EB/2008/Volume3/EB-08C00009A.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    3. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    4. John K.-H Quah, 2007. "The Comparative Statics of Constrained Optimization Problems," Econometrica, Econometric Society, vol. 75(2), pages 401-431, March.
    5. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    6. Marco LiCalzi & Arthur F. Veinott, 2005. "Subextremal functions and lattice programming," GE, Growth, Math methods 0509001, University Library of Munich, Germany.
    7. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Koji Shirai, 2009. "A generalization of monotone comparative statics: Correction," Economics Bulletin, AccessEcon, vol. 29(1), pages 116-121.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Elena Antoniadou & Leonard J Mirman & Richard Ruble, 2014. "Lattices and Lotteries," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 445-463, May.
    4. Uttiya Paul & Tarun Sabarwal, 2023. "Directional monotone comparative statics in function spaces," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(1), pages 153-169, April.
    5. Nikolai Kukushkin, 2015. "The single crossing conditions for incomplete preferences," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 225-251, February.
    6. Roy, Sunanda & Sabarwal, Tarun, 2012. "Characterizing stability properties in games with strategic substitutes," Games and Economic Behavior, Elsevier, vol. 75(1), pages 337-353.
    7. repec:kan:wpaper:201412 is not listed on IDEAS
    8. Kukushkin, Nikolai S., 2013. "Approximate Nash equilibrium under the single crossing conditions," MPRA Paper 44320, University Library of Munich, Germany.
    9. Sobel, Joel, 2019. "Iterated weak dominance and interval-dominance supermodular games," Theoretical Economics, Econometric Society, vol. 14(1), January.
    10. Shuoxun Zhang & Tarun Sabarwal & Li Gan, 2015. "Strategic Or Nonstrategic: The Role Of Financial Benefit In Bankruptcy," Economic Inquiry, Western Economic Association International, vol. 53(2), pages 1004-1018, April.
    11. 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.
    12. Roy, Sunanda & Sabarwal, Tarun, 2010. "Monotone comparative statics for games with strategic substitutes," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 793-806, September.
    13. Koji Shirai, 2013. "Welfare variations and the comparative statics of demand," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(2), pages 315-333, June.
    14. Kukushkin, Nikolai S., 2018. "Better response dynamics and Nash equilibrium in discontinuous games," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 68-78.
    15. Wang, Jianli & Li, Jingyuan, 2016. "Lattice-based monotone comparative statics on saving with Selden/Kreps–Porteus preferences," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 132-138.
    16. Andrew J. Monaco & Tarun Sabarwal, 2016. "Games with strategic complements and substitutes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(1), pages 65-91, June.
    17. repec:kan:wpaper:201502 is not listed on IDEAS
    18. Łukasz Balbus & Paweł Dziewulski & Kevin Reffett & Łukasz Woźny, 2019. "A qualitative theory of large games with strategic complementarities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 497-523, April.
    19. Koch, Caleb M., 2019. "Index-wise comparative statics," Mathematical Social Sciences, Elsevier, vol. 102(C), pages 35-41.
    20. Chambers, Christopher P. & Echenique, Federico, 2009. "Supermodularity and preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1004-1014, May.
    21. Rabah Amir, 2018. "Special issue: supermodularity and monotone methods in economics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 547-556, October.
    22. Diego C. Nocetti, 2016. "Robust Comparative Statics of Risk Changes," Management Science, INFORMS, vol. 62(5), pages 1381-1392, May.

    More about this item

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ebl:ecbull:eb-08c00009. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: John P. Conley (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.