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Switching surfaces inN-person differential games

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Abstract

Switching surfaces inN-person differential games are essentially similar to those encountered in optimal control and two-person, zero-sum differential games. The differences between the Nash noncooperative solution and the saddle-point solution are reflected in the dispersal surfaces. These are discussed through classification and construction procedures for switching surfaces. A simple example of a two-person, nonzero-sum game is considered. A complete solution of this game will be presented in a companion paper (Ref. 1).

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References

  1. Prasad, U. R., andSarma, I. G.,An Example of a Two-Person Nonzero-Sum Differential Game (to appear).

  2. Karvovskiy, G. S., andKuznetsov, A. D.,A Maximum Principle for NPlayers, Engineering Cybernetics, No. 6, 1966.

  3. Case, J. H.,Toward a Theory of Many Player Differential Games, SIAM Journal on Control, Vol. 7, No. 1, 1969.

  4. Starr, A. W., andHo, Y. C.,Nonzero-Sum Differential Games, Journal of Optimization Theory and Applications, Vol. 3, No. 3, 1969.

  5. Starr, A. W., andHo, Y. C.,Further Properties of Nonzero-Sum Differential Games, Journal of Optimization Theory and Applications, Vol. 3, No. 4, 1969.

  6. Sarma, I. G., Ragade, R. K., andPrasad, U. R.,Necessary Conditions for Optimal Strategies in a Class of Noncooperative N-Person Differential Games, SIAM Journal on Control, Vol. 7, No. 4, 1969.

  7. Isaacs, R.,Differential Games, John Wiley and Sons, New York, 1965.

    Google Scholar 

  8. Berkovitz, L. D.,Variational Methods in Problems of Control and Programming, Journal of Mathematical Analysis and Applications, Vol. 3, No. 1, 1961.

  9. Isaacs, R.,Differential Games: Their Scope, Nature, and Future, Journal of Optimization Theory and Applications, Vol. 3, No. 5, 1969.

  10. Johnson, C. D.,Singular Solutions in Problems of Automatic Control, Advances in Control Systems, Vol. 2, Edited by C. T. Leondes, Academic Press, New York, 1965.

    Google Scholar 

  11. Kelley, H. J., Kopp, R. E., andMoyer, H. G.,Singular Extremals, Topics in Optimization, Edited by G. Leitmann, Academic Press, New York, 1966.

    Google Scholar 

  12. Robbins, H. M.,A Generalized Legendre-Clebsch Condition for the Singular Cases in Optimal Control, IBM Journal of Research and Development, Vol. 11, No. 4, 1967.

  13. Anderson, G. M.,Necessary Conditions for Singular Solutions in Differential Games with Controls Appearing Linearly, Paper presented at the First International Conference of the Theory and Applications of Differential Games, Amherst, Massachusetts, 1969.

  14. Berkovitz, L. D.,A Variational Approach to Differential Games, Advances in Game Theory, Edited by M. Dresher, L. S. Shapley, and A. W. Tucker, Annals of Mathematical Studies, No. 52, Princeton University Press, Princeton, New Jersey, 1964.

    Google Scholar 

  15. Leitmann, G., Editor,Topics in Optimization, Academic Press, New York, 1967.

    Google Scholar 

  16. Leitmann, G.,An Introduction to Optimal Control, McGraw-Hill Book Company, New York, 1966.

    Google Scholar 

  17. Breakwell, J. V., andMerz, A. W.,Toward a Complete Solution of the Homicidal Chauffeur Game, Paper presented at the First International Conference on the Theory and Applications of Differential Games, Amherst, Massachusetts, 1969.

  18. Sarma, I. G., andPrasad, U. R.,Optimal Control Problems with Multiple Criteria (to appear).

  19. Luce, R. D., andRaiffa, H.,Games and Decisions, John Wiley and Sons, New York, 1957.

    Google Scholar 

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Authors and Affiliations

  1. School of Automation, Indian Institute of Science, Bangalore, India

    I. G. Sarma (Professor)

  2. Department of Aeronautical Engineering, Indian Institute of Science, Bangalore, India

    U. R. Prasad (Senior Research Fellow)

Authors
  1. I. G. Sarma
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  2. U. R. Prasad
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Communicated by G. Leitmann

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Sarma, I.G., Prasad, U.R. Switching surfaces inN-person differential games. J Optim Theory Appl 10, 160–177 (1972). https://doi.org/10.1007/BF00934731

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  • DOI: https://doi.org/10.1007/BF00934731

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