Non—Cooperative Differential Games

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


Here we shall consider non-cooperative play in the sense of Nash. Again, we shall restate the definitions and results of Chapter 1 as they apply to the situation discussed in Chapter 2.


Nash Equilibrium Collective Bargaining Differential Game Transversality Condition Admissible Strategy 
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References for Chapter 4

  1. [4.1]
    Ciletti, M.D., Differential Games with Information Time Lag, in Topics in Differential: Games (ed. E. Blaquière, A.), North Holland, Amsterdam, 1973.Google Scholar
  2. [4.2]
    Blaquière, A., Differential Games with Time Lag, in Techniques of Optimization (ed. Balakrishnan, A.V.) Academic Press, N.Y., 1972.Google Scholar
  3. 3J Case, J.H., Toward a Theory of Many Player Differential Games, SIAM J. Control, Vol. 7, No. 2, 1969.Google Scholar
  4. [4.4]
    Leitmann, G. Differential Games, in Differential Games: Theory and Applications (eds. Ciletti, M.D. and Starr, A.W. ), ASME, N.Y., 1970Google Scholar
  5. [4.5]
    Ho, Y.C. and Starr, A.W., Nonzero-Sum Differential Games, J. Optim. Theory Appl., Vol. 3, No. 3, 1969.Google Scholar
  6. [4.6]
    Ho, Y.C. and Starr, A.W., Further Properties of Nonzero-Sum Differential Games, J. Optim. Theory Appl., Vol. 3, No. 4, 1969.Google Scholar
  7. [4.7]
    Isaacs, R., Differential Games Wiley, N.Y., 1965.Google Scholar
  8. [4.8]
    Berkovitz, L.D., Necessary Conditions for Optimal Strategies in a Class of Differential Games and Control Problems, SIAM J. Control, Vol. 5, No. 1, 1967.Google Scholar
  9. [4.9]
    Blaquière, A., Gérard, F., and Leitmann, G., Quantitative and Qualitative Games, Academic Press, N.Y., 1969.MATHGoogle Scholar
  10. [4.10
    Leitmann, G. and Mon, G., On a Class of Differential Games, in Advanced Problems and Methods for Space Flight Optimization (ed. Fraeijs de Veubecke) Pergamon, N.Y., 1969.Google Scholar
  11. [4.11]
    Blaquière, A. and Leitmann, G., Jeux Quantitatifs Gauthier-Villars, Paris, 1969Google Scholar
  12. [4.12]
    Stalford, H. and Leitmann, G. Sufficiency Conditions for Nash Equilibria in N-Person Differential Games, in Topics in Differential Games (ed. A. Blaquière), North-Holland, Amsterdam, 1973.Google Scholar
  13. [4.13]
    Leitmann, G. and Stalford, H., Sufficiency for Optimal Strategies in Nash Equilibrium Games, in Techniques of Optimization (ed. A. V. Balakrishnan ), Academic Press, N.Y., 1971.Google Scholar

Copyright information

© Springer-Verlag Wien 1974

Authors and Affiliations

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

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