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Coordinate Transformations and Derivation of Open-Loop Nash Equilibria

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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.

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References

  1. Leitmann, G., A Note on Absolute Extrema of Certain Integrals, International Journal of Nonlinear Mechanics, Vol. 2, pp. 55-59, 1967.

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  2. Leitmann, G., The Calculus of Variations and Optimal Control, Plenum Publishing Corporation, New York, NY, 1981.

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  3. Leitmann, G., On a Class of Direct Optimization Problems, Journal of Optimization Theory and Applications, Vol. 108, pp. 467-481, 2001.

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  4. Haurie, A., and Leitmann, G., On the Global Asymptotic Stability of Equilibrium Solutions for Open-Loop Differential Games, Journal of Large Scale Systems, Vol. 6, pp. 107-122, 1984.

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  5. Dockner, E. J., JØr gensen, S., van Long, N., and Sorger, G., Differential Games in Economics and Management Science, Cambridge University Press, Cambridge, England, 2000.

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Authors and Affiliations

  1. Department of Business Studies, University of Vienna, Vienna, Austria

    E. J. Dockner (Professor of Business Administration)

  2. College of Engineering, University of California, Berkeley, California

    G. Leitmann (Professor in the Graduate School)

Authors
  1. E. J. Dockner
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  2. G. Leitmann
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Dockner, E.J., Leitmann, G. Coordinate Transformations and Derivation of Open-Loop Nash Equilibria. Journal of Optimization Theory and Applications 110, 1–15 (2001). https://doi.org/10.1023/A:1017511827387

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  • DOI: https://doi.org/10.1023/A:1017511827387

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