IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v123y2004i1d10.1023_bjota.0000043990.32923.ac.html
   My bibliography  Save this article

An Extension of the Coordinate Transformation Method for Open-Loop Nash Equilibria

Author

Listed:
  • D. A. Carlson

    (University of Toledo)

  • G. Leitmann

    (University of California)

Abstract

In Leitmann (Ref. 1), a coordinate transformation method was introduced to obtain global solutions for free problems in the calculus of variations. This direct method was extended and broadened in Carlson (Ref. 2) and later in Leitmann (Ref. 3). The applicability of the original work of Leitmann (Ref. 1) was further developed in Dockner and Leitmann (Ref. 4) to include the class of open-loop dynamic games. In the present work, we improve the results of Ref. 4 in two directions. First, we enlarge the class of open-loop dynamic games to permit coupling among the dynamic equations via the states of the players; second, we incorporate the modifications given in Refs. 2 and 3. Our results greatly increase the applicability of this method. An example arising from the harvesting of a renewable resource is presented to illustrate the utility of our results.

Suggested Citation

  • D. A. Carlson & G. Leitmann, 2004. "An Extension of the Coordinate Transformation Method for Open-Loop Nash Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 123(1), pages 27-47, October.
    • Handle: RePEc:spr:joptap:v:123:y:2004:i:1:d:10.1023_b:jota.0000043990.32923.ac
    DOI: 10.1023/B:JOTA.0000043990.32923.ac
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/B:JOTA.0000043990.32923.ac
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/B:JOTA.0000043990.32923.ac?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. E. J. Dockner & G. Leitmann, 2001. "Coordinate Transformations and Derivation of Open-Loop Nash Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 110(1), pages 1-15, July.
    2. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(4), pages 1007-1017, August.
    3. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1461-1465, December.
    4. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(1), pages 193-194, February.
    5. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(5), pages 1273-1289, October.
    6. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(3), pages 819-821, June.
    7. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(2), pages 541-545, April.
    8. D.A. Carlson, 2002. "An Observation on Two Methods of Obtaining Solutions to Variational Problems," Journal of Optimization Theory and Applications, Springer, vol. 114(2), pages 345-361, August.
    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. Jiangjing Zhou & Anna Tur & Ovanes Petrosian & Hongwei Gao, 2021. "Transferable Utility Cooperative Differential Games with Continuous Updating Using Pontryagin Maximum Principle," Mathematics, MDPI, vol. 9(2), pages 1-22, January.
    2. Mojtaba Dehghan Banadaki & Hamidreza Navidi, 2020. "Numerical Solution of Open-Loop Nash Differential Games Based on the Legendre Tau Method," Games, MDPI, vol. 11(3), pages 1-11, July.
    3. S. G. Ji & S. Y. Shi, 2006. "Periodic Solutions for a Class of Second-Order Ordinary Differential Equations," Journal of Optimization Theory and Applications, Springer, vol. 130(1), pages 125-137, July.

    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. S. G. Ji & S. Y. Shi, 2006. "Periodic Solutions for a Class of Second-Order Ordinary Differential Equations," Journal of Optimization Theory and Applications, Springer, vol. 130(1), pages 125-137, July.
    2. D. F. M. Torres & G. Leitmann, 2008. "Contrasting Two Transformation-based Methods for Obtaining Absolute Extrema," Journal of Optimization Theory and Applications, Springer, vol. 137(1), pages 53-59, April.
    3. F. O. O. Wagener, 2009. "On the Leitmann Equivalent Problem Approach," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 229-242, July.
    4. Wagener, F.O.O., 2009. "On conjugate points and the Leitmann equivalent problem approach," CeNDEF Working Papers 09-08, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    5. A. B. Malinowska & D. F. M. Torres, 2010. "The Hahn Quantum Variational Calculus," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 419-442, December.
    6. Claudia García-García & Catalina B. García-García & Román Salmerón, 2021. "Confronting collinearity in environmental regression models: evidence from world data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 895-926, September.
    7. Cambier, Adrien & Chardy, Matthieu & Figueiredo, Rosa & Ouorou, Adam & Poss, Michael, 2022. "Optimizing subscriber migrations for a telecommunication operator in uncertain context," European Journal of Operational Research, Elsevier, vol. 298(1), pages 308-321.
    8. Libura, Marek, 2007. "On the adjustment problem for linear programs," European Journal of Operational Research, Elsevier, vol. 183(1), pages 125-134, November.
    9. Christophe Loussouarn & Carine Franc & Yann Videau & Julien Mousquès, 2021. "Can General Practitioners Be More Productive? The Impact of Teamwork and Cooperation with Nurses on GP Activities," Health Economics, John Wiley & Sons, Ltd., vol. 30(3), pages 680-698, March.
    10. Tschakert, Petra, 2016. "Shifting Discourses of Vilification and the Taming of Unruly Mining Landscapes in Ghana," World Development, Elsevier, vol. 86(C), pages 123-132.
    11. María-Consuelo Casabán & Rafael Company & Lucas Jódar, 2020. "Non-Gaussian Quadrature Integral Transform Solution of Parabolic Models with a Finite Degree of Randomness," Mathematics, MDPI, vol. 8(7), pages 1-16, July.
    12. Isabelle Boutron & Peter John & David J. Torgerson, 2010. "Reporting Methodological Items in Randomized Experiments in Political Science," The ANNALS of the American Academy of Political and Social Science, , vol. 628(1), pages 112-131, March.
    13. Ben Slimane, Faten & Padilla Angulo, Laura, 2019. "Strategic change and corporate governance: Evidence from the stock exchange industry," Journal of Business Research, Elsevier, vol. 103(C), pages 206-218.
    14. Bossert, Walter & Derks, Jean & Peters, Hans, 2005. "Efficiency in uncertain cooperative games," Mathematical Social Sciences, Elsevier, vol. 50(1), pages 12-23, July.
    15. Weijun Xie & Yanfeng Ouyang & Sze Chun Wong, 2016. "Reliable Location-Routing Design Under Probabilistic Facility Disruptions," Transportation Science, INFORMS, vol. 50(3), pages 1128-1138, August.
    16. Sin-Yu Ho & N.M. Odhiambo, 2018. "Analysing the macroeconomic drivers of stock market development in the Philippines," Cogent Economics & Finance, Taylor & Francis Journals, vol. 6(1), pages 1451265-145, January.
    17. Natalia Nikolaevna Natocheeva* & Yuri Alexandrovich Rovensky & Yuri Yuryevich Rusanov & Tatiana Viktorovna Belyanchikova & Anna Anatolevna Staurskaya, 2018. "Optimizing Variability of Approaches to Regulatory Financing of Higher Education Services," The Journal of Social Sciences Research, Academic Research Publishing Group, pages 221-227:3.
    18. Philip Arestis & Howard Stein, 2005. "An Institutional Perspective to Finance and Development as an Alternative to Financial Liberalisation," International Review of Applied Economics, Taylor & Francis Journals, vol. 19(4), pages 381-398.
    19. Sahar Validi & Arijit Bhattacharya & P. J. Byrne, 2020. "Sustainable distribution system design: a two-phase DoE-guided meta-heuristic solution approach for a three-echelon bi-objective AHP-integrated location-routing model," Annals of Operations Research, Springer, vol. 290(1), pages 191-222, July.
    20. Cabada, Alberto & Fernández-Gómez, Carlos, 2015. "Constant sign solutions of two-point fourth order problems," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 122-133.

    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:spr:joptap:v:123:y:2004:i:1:d:10.1023_b:jota.0000043990.32923.ac. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.