Cooperative Differential Games

  • George Leitmann
Part of the International Centre for Mechanical Sciences book series (CISM, volume 190)


Here we shall consider cooperative play in the sense of Pareto. In particular, we shall restate the definitions and results of Chapter 1 as they apply to the situation discussed in Chapter 2. The definition of Pareto-optimality, Definition 1.1, becomes


Optimal Control Problem Cooperative Game Differential Game Optimal Control Theory Terminal Time 
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References for Chapter 3

  1. [3.1]
    Leitmann, G., A Note on Optimal Open-Loop and Closed-Loop Control, J. Dynamical Systems, Measurement, and Control, Vol. 98, No. 3, 1974.Google Scholar
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    Da Cunha, N.O. and Polak, E., Constrained Minimization under Vector-Valued Criteria in Linear Topological Spaces, in Mathematical Theory of Control (eds. Balakrishnan, A.V. and Neustadt, L.W. ), Academic Press, N. Y. 1967.Google Scholar
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    Vincent, T.L. and Leitmann, G., Control Space Properties of Cooperative Games, J. Optim. Theory Appl., Vol. 6, No. 2, 1970.Google Scholar
  4. [3.4]
    Leitmann, G., Rocklin, S., and Vincent, T.L., A Note on Control Space Properties of Cooperative Games, J. Optim. Theory Appl., Vol. 9, No. 6, 1972.Google Scholar
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    Stalford, H., Criteria for Pareto-optimality in Cooperative Differential Games, J. Optim. Theory Appl., Vol. 9, No. 6. 1972.Google Scholar
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    Blaquière, A., Juricek, L., and Wiese, K., Geometry of Pareto Equilibria and a Maximum Principle in N-Person Differential Games, J. Math. Anal. Appl. Vol. 38, No., 1, 1972.Google Scholar
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    Pontryagin, L.S., Boltynskii, V.G., Gamkrelidze, R.V., and Mishchenko, E.F., The Mathematical Theory of Optimal Processes Interscience Publ., N. Y., 1962.Google Scholar
  8. [3.8]
    Athans, M. and Falb, P.L., Optimal Control,McGraw-Hill, N. Y., 1966.Google Scholar
  9. [3.9]
    Leitmann, G., An Introduction to Optimal Control McGraw-Hill, N. Y., 1966.Google Scholar
  10. [3.10]
    Leitmann, G., and Stalford, H., A Sufficiency Theorem for Optimal Control J. Optim. Theory Appl., Vol. 8, No. 3, 1971.Google Scholar
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    Mangasarian, O.L., Sufficient Conditions for the Optimal Control of Nonlinear Systems, SIAM J. Control, Vol. 4, No. 1, 1966.Google Scholar
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    Leitmann, G., and Schmitendorf, W., Some Sufficiency Conditions for Pareto-optimal Control, J. Dynamical Systems, Measurement and Control, Vol. 95, No. 3, 1963.Google Scholar
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    Leitmann, G., Sufficiency for Optimal Control, J. Optim. Theory Appl., Vol. 2, No. 5, 1968.Google Scholar
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    Stalford, H., Sufficient Conditions for Optimal Control with State and Control Constraints, J. Optm. Theory Appl., Vol. 7, No. 2, 1971.Google Scholar
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    Leitmann, G., and Liu, P.T., A Differential Game Model of Labor-Management Negotiation During a Strike, J. Optim. Theory Appl. Vol. 13, No. 4, 1974.Google Scholar
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    Starr, A.W., Non-zero Sum Differential Games: Concepts and Models, Division of Engineering and Applied Physics Tech.Report 590, Harvard University, Cambridge, 1969.Google Scholar

Copyright information

© Springer-Verlag Wien 1974

Authors and Affiliations

  • George Leitmann
    • 1
  1. 1.University of CaliforniaBerkeleyUSA

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