IDEAS home Printed from https://ideas.repec.org/p/drm/wpaper/2012-41.html
   My bibliography  Save this paper

The Ricardo-Lemke parametric algorithm on oddity and uniqueness

Author

Listed:
  • Christian Bidard

Abstract

The parametric Lemke algorithm finds an odd number of solutions to the linear complementarity problem LCP (q, M), for a matrix M with zero blocks on the diagonal and vector q within a certain domain. A criterion for monotonicity and uniqueness is given. The algorithm applies to the determination of a long-run equilibrium in the presence of scarce resources, and its first description can be traced back to the nineteenth century economist David Ricardo.

Suggested Citation

  • Christian Bidard, 2012. "The Ricardo-Lemke parametric algorithm on oddity and uniqueness," EconomiX Working Papers 2012-41, University of Paris Nanterre, EconomiX.
    • Handle: RePEc:drm:wpaper:2012-41
    as

    Download full text from publisher

    File URL: http://economix.fr/pdf/dt/2012/WP_EcoX_2012-41.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
    2. Christian Bidard, 2012. "The Frail Grounds of the Ricardian Dynamics," EconomiX Working Papers 2012-43, University of Paris Nanterre, EconomiX.
    3. Salvadori, Neri, 1986. "Land and Choice of Techniques within the Sraffa Framework," Australian Economic Papers, Wiley Blackwell, vol. 25(46), pages 94-105, June.
    4. Christian Bidard & Guido Erreygers, 1998. "The number and type of long-term equilibria," Journal of Economics, Springer, vol. 67(2), pages 181-205, June.
    5. Dantzig, George B. & Manne, Alan S., 1974. "A complementarity algorithm for an optimal capital path with invariant proportions," Journal of Economic Theory, Elsevier, vol. 9(3), pages 312-323, November.
    Full references (including those not matched with items on IDEAS)

    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. Christian Bidard, 2012. "The Ricardo-Lemke parametric algorithm on oddity and uniqueness," Working Papers hal-04141043, HAL.
    2. Christian Bidard, 2012. "Ricardo And Lemke," Working Papers hal-04141029, HAL.
    3. Christian Bidard, 2012. "Ricardo And Lemke," EconomiX Working Papers 2012-48, University of Paris Nanterre, EconomiX.
    4. Bidard, Christian, 2014. "The Ricardian rent theory: an overview," Centro Sraffa Working Papers CSWP8, Centro di Ricerche e Documentazione "Piero Sraffa".
    5. Christian Bidard, 2014. "The Wage Curve in Austrian Models," EconomiX Working Papers 2014-54, University of Paris Nanterre, EconomiX.
    6. Christian Bidard, 2014. "The Ricardian rent theory two centuries after," Working Papers hal-04141289, HAL.
    7. Christian Bidard, 2014. "The Ricardian rent theory two centuries after," EconomiX Working Papers 2014-54, University of Paris Nanterre, EconomiX.
    8. Christian Bidard, 2012. "The Frail Grounds of the Ricardian Dynamics," Working Papers hal-04141039, HAL.
    9. Christian Bidard, 2015. "An oddity property for cross-dual games," EconomiX Working Papers 2015-4, University of Paris Nanterre, EconomiX.
    10. Christian Bidard, 2012. "The Frail Grounds of the Ricardian Dynamics," EconomiX Working Papers 2012-43, University of Paris Nanterre, EconomiX.
    11. Christian Bidard, 2011. "The Ricardian Dynamics Revisited," Working Papers hal-04140981, HAL.
    12. Christian Bidard, 2015. "An oddity property for cross-dual games," Working Papers hal-04141427, HAL.
    13. van der Laan, G. & Talman, A.J.J. & Yang, Z.F., 2005. "Computing Integral Solutions of Complementarity Problems," Other publications TiSEM b8e0c74e-2219-4ab0-99a2-0, Tilburg University, School of Economics and Management.
    14. Zhang, Bin, 2012. "Multi-tier binary solution method for multi-product newsvendor problem with multiple constraints," European Journal of Operational Research, Elsevier, vol. 218(2), pages 426-434.
    15. Baohua Huang & Wen Li, 2023. "A smoothing Newton method based on the modulus equation for a class of weakly nonlinear complementarity problems," Computational Optimization and Applications, Springer, vol. 86(1), pages 345-381, September.
    16. Talman, A.J.J. & van der Heyden, L., 1981. "Algorithms for the linear complementarity problem which allow an arbitrary starting point," Research Memorandum FEW 99, Tilburg University, School of Economics and Management.
    17. Bernhard von Stengel & Antoon van den Elzen & Dolf Talman, 2002. "Computing Normal Form Perfect Equilibria for Extensive Two-Person Games," Econometrica, Econometric Society, vol. 70(2), pages 693-715, March.
    18. R. B. Bapat & S. K. Neogy, 2016. "On a quadratic programming problem involving distances in trees," Annals of Operations Research, Springer, vol. 243(1), pages 365-373, August.
    19. Frederic Murphy & Axel Pierru & Yves Smeers, 2016. "A Tutorial on Building Policy Models as Mixed-Complementarity Problems," Interfaces, INFORMS, vol. 46(6), pages 465-481, December.
    20. Edward J. Balistreri & Maryla Maliszewska & Israel Osorio-Rodarte & David G. Tarr & Hidemichi Yonezawa, 2016. "Poverty and Shared Prosperity Implications of Reducing Trade Costs Through Deep Integration in Eastern and Southern Africa," Working Papers 2016-07, Colorado School of Mines, Division of Economics and Business.

    More about this item

    Keywords

    Oddity; parametric Lemke algorithm; Ricardo; uniqueness;
    All these keywords.

    JEL classification:

    • B12 - Schools of Economic Thought and Methodology - - History of Economic Thought through 1925 - - - Classical (includes Adam Smith)
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:drm:wpaper:2012-41. 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: Valerie Mignon (email available below). General contact details of provider: https://edirc.repec.org/data/modemfr.html .

    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.