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Coordinate Transformations and Derivation of Open-Loop Nash Equilibria

Author

Listed:
  • E. J. Dockner

    (University of Vienna)

  • G. Leitmann

    (University of California)

Abstract

Leitmann (Ref. 1) introduced coordinate transformations to derive global optima of a class of dynamic optimization problems. We present applications of this method to derive open-loop Nash equilibria for finite-time horizon differential games. The method of coordinate transformations is especially useful in cases where the original game does not satisfy the global curvature conditions normally imposed in sufficient optimality conditions.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:110:y:2001:i:1:d:10.1023_a:1017511827387
    DOI: 10.1023/A:1017511827387
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    References listed on IDEAS

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    1. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, October.
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    Cited by:

    1. 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.
    2. 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.
    3. David Yeung, 2014. "Dynamically consistent collaborative environmental management with production technique choices," Annals of Operations Research, Springer, vol. 220(1), pages 181-204, September.
    4. 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.
    5. L. Colombo & L. Lambertini, 2003. "Dynamic Advertising Under Vertical Product Differentiation," Journal of Optimization Theory and Applications, Springer, vol. 119(2), pages 261-280, November.

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