Skip to main content

Multiple-stage quantitative games

Part of the Lecture Notes in Mathematics book series (LNM,volume 112)

Keywords

  • Optimal Path
  • Tangent Plane
  • Differential Game
  • Geometric Aspect
  • Strategy Pair

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

1. On the Geometry of Optimal Processes

  1. A. BLAQUIERE and G. LEITMANN, On the Geometry of Optimal Processes, Parts I,II, III, Univ. of California, Berkeley, IER Repts. AM-64-10, AM-65-11, AM-66-1.

    Google Scholar 

  2. G. LEITMANN, Some Geometrical Aspects of Optimal Processes, J. SIAM, Ser. A: Control 3, No. 1, 1965

    Google Scholar 

  3. A. Blaquiere, Further Investigation into the Geometry of Optimal Processes, J. SIAM, Ser. A: Control 3, No. 2, 1965

    Google Scholar 

  4. A. BLAQUIERE and G. LEITMANN, Some Geometric Aspects of Optimal Processes, Part I: Problems with Control Constraints, Proc.Congr. Automatique Théorique, Paris 1965, Dunod Ed.

    Google Scholar 

  5. A. BLAQUIERE and G. LEITMANN, On the Geometry of Optimal Processes, in Topics in Optimization, Academic Press, 1967, pp. 265–371 (G. Leitmann ed.)

    Google Scholar 

  6. K.V. SAUNDERS and G. LEITMANN, Some Geometric Aspects of Optimal Processes, Part II: Problems with State Constraints, Proc.Congr. Automatique Théorique, Paris 1965, Dunod Ed.

    Google Scholar 

  7. H. HALKIN, The Principle of Optimal Evolution, in Nonlinear Differential Equations and Nonlinear Mechanics, Academic Press, 1963 (J.P. LaSalle and S. Lefschetz, eds.)

    Google Scholar 

  8. H. HALKIN, Mathematical Foundations of System Optimization, in Topics in Optimization, Academic Press, 1967, pp. 198–260, (G. Leitmann ed.)

    Google Scholar 

  9. E. ROXIN, A Geometric Interpretation of Pontryagin's Maximum Principle, in Nonlinear Differential Equations and Nonlinear Mechanics, Academic Press, 1963, (J.P. LaSalle and S. Lefschetz, eds.)

    Google Scholar 

  10. R.E. BELLMAN, Dynamic Programming, Princeton Univ. Press, Princeton, New Jersey, 1957

    MATH  Google Scholar 

  11. A. BLAQUIERE and G. LEITMANN, Further Geometric Aspects of Optimal Processes: Multiple-Stage Dynamic Systems, Mathematical Theory of Control, Academic Press, 1967

    Google Scholar 

2. On the Theory of Games

  1. J. von NEUMANN and O. MORGENSTERN, Theory of Games and Economic Behavior, Princeton Univ. Press, Princeton, New Jersey, 1953

    MATH  Google Scholar 

  2. J. MAC KINSEY, An Introduction to the Theory of Games, McGraw-Hill, 1952

    Google Scholar 

  3. L. ZADEH, Optimality and Nonscalar-valued Performance Criteria, IEEE Transactions on Automatic Control, Vol. Ac-8, Jan. 1963, pp. 59–60

    CrossRef  Google Scholar 

  4. R. ISAACS, Differential Games, Wiley, N.Y. 1965

    MATH  Google Scholar 

  5. L.D. BERKOVITZ, A Variational Approach to Differential Games, in Advances in Game Theory, Princeton Univ. Press, Princeton, 1964, pp. 127–174

    Google Scholar 

  6. L.D. BERKOVITZ and W.H. FLEMING, On Differential Games with Integral Payoff, in Contributions to the Theory of Games III, Princeton Univ. Press, Princeton, 1957, pp. 413–435

    Google Scholar 

  7. L.D. BERKOVITZ, Necessary Conditions for Optimal Strategies in a Class of Differential Games and Control Problems, J. SIAM Control, Vol. 5, No. 1, 1967, pp. 1–24

    MathSciNet  MATH  Google Scholar 

  8. D.L. KELENDZHERIDZE, A Pursuit Problem, in The Mathematical Theory of Optimal Processes, Interscience, N.Y., 1962

    Google Scholar 

  9. L.S. PONTRYAGIN, On Some Differential Games, J. SIAM Control, Vol. 3, No. 1, 1965, pp. 49–52

    MathSciNet  MATH  Google Scholar 

  10. L.S. PONTRYAGIN, On the Theory of Differential Games, Uspehi Mat. Nauk 21, No. 4 (130), 1966, pp. 219–274

    MathSciNet  MATH  Google Scholar 

  11. E.F. MISHCHENKO and L.S. PONTRYAGIN, Linear Differential Games, Dokl.Akad.Nauk SSSR, Tom 174, No. 1, 1967, pp. 27–29, and Soviet Math. Dokl. Vol. 8, No. 3, 1967, pp. 585–588

    MathSciNet  Google Scholar 

  12. Y.C. HO, A.E. BRYSON and S. BARON, Differential Games and Optimal Pursuit-Evasion Strategies, IEEE Transactions on Automatic Control, Vol. AC-10, October 1965, pp. 385–389

    CrossRef  MathSciNet  Google Scholar 

  13. S. BARON, Differential Games and Optimal Pursuit-Evasion Strategies, Ph.D. Thesis in Applied Mathematics, Harvard University, Cambridge, 1966

    Google Scholar 

  14. E.N. SIMAKOVA, Differential Games (a survey paper), Avtomatika i Telemekhanika, Vol. 27, No. 11, Nov. 1966, pp. 161–178

    MathSciNet  Google Scholar 

  15. I.G. SARMA and R.K. RAGADE, Some Considerations in Formulating Optimal Control Problems as Differential Games, Int.J.Control, Vol. 4, No. 3, 1966, pp. 265–279

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. A. KAUFMANN, Graphs, Dynamic Programming, and Finite Games, Academic Press, 1967

    Google Scholar 

  17. G. LEITMANN and G. MON, Some Geometric Aspects of Differential Games, Journal of Astronautical Sciences, Vol. 14, No. 2, Mar.–Apr., 1967, pp. 56–65

    MathSciNet  Google Scholar 

  18. G. LEITMANN and G. MON, On a Class of Differential Games, Proceed. Colloquium on Advanced Problems and Methods for Space Flight Optimization, Liege 1967, Pergamon Press 1968 (also in Kibernetika, Jan. 1968)

    Google Scholar 

  19. A. BLAQUIERE and G. LEITMANN, Quantitative Games, Mémorial des Sciences Mathématiques, Gauthier-Villars Ed. 1968

    Google Scholar 

  20. A. BLAQUIERE, Quantitative and Qualitative Games, A Geometric Approach — Part I: Quantitative Games Report, Laboratoire d'Automatique Théorique, Faculté des Sciences de Paris, 1968

    Google Scholar 

  21. A. BLAQUIERE, F. GERARD and G. LEITMANN, Quantitative and Qualitative Games, A Geometric Approach, Academic Press, 1969

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1970 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Blaquière, A., Leitmann, G. (1970). Multiple-stage quantitative games. In: Moiseev, N.N. (eds) Colloquium on Methods of Optimization. Lecture Notes in Mathematics, vol 112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0060197

Download citation

  • DOI: https://doi.org/10.1007/BFb0060197

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-04901-2

  • Online ISBN: 978-3-540-36204-3

  • eBook Packages: Springer Book Archive