Skip to main content
Log in

Axiomatic approach in differential games

  • Contributed Papers
  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

Differential games are usually defined by differential equations. Recently, some work has been done on the possibility of defining such games in a more general, axiomatic way. In this paper, the advantages of this approach are discussed and possible further developments are pointed out.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

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

    Google Scholar 

  2. Berkovitz, L. D.,A Survey of Differential Games, Mathematical Theory of Control, Edited by A. V. Balakrishnan and L. W. Neustadt, Academic Press, New York, 1967.

    Google Scholar 

  3. Varaiya, P. P.,The Existence of Solutions to a Differential Game, SIAM Journal on Control, Vol. 5, No. 1, 1967.

  4. Bushaw, D.,Dynamical Polysystems—A Survey, US-Japan Seminar on Differential and Functional Equations, Edited by W. A. Harris, Jr., and Y. Sibuya, W. A. Benjamin, New York, 1957.

    Google Scholar 

  5. Roxin, E.,On Generalized Dynamical Systems Defined by Contingent Equations, Journal of Differential Equations, Vol. 1, No. 2, 1965.

  6. Roxin, E.,Stability in General Control Systems, Journal of Differential Equations, Vol. 1, No. 2, 1965.

  7. Bushaw, D.,Dynamical Polysystems and Optimization, Contributions to Differential Equations, Vol. 2, No. 3, 1963.

  8. Barbashin, E. A.,On the Theory of Generalized Dynamical Systems, Učenye Zapiski Moskovskogo Gosudarstvennyi Universitet No. 135, 1949.

  9. Kirillova, F. M.,The Application of Functional Analysis to Problems of Pursuit, Mathematical Theory of Control, Edited by A. V. Balakrishnan and L. W. Neustadt, Academic Press, New York, 1967.

    Google Scholar 

  10. Varaiya, P. P., andLin, J.,Existence of Saddle Points in Differential Games, University of California at Berkeley, Electronics Research Laboratory, Memorandum No. ERL-M241, 1968.

  11. Roxin, E.,On Varaiya's Definition of a Differential Game, US-Japan Seminar on Differential and Functional Equations, Edited by W. A. Harris, Jr., and Y. Sibuya, W. A. Benjamin, New York, 1967.

    Google Scholar 

  12. Dunford, N., andSchwartz, J. T.,Linear Operators, Part 1, John Wiley and Sons (Interscience Publishers), New York.

  13. Pontryagin, L. S.,On Some Differential Games, SIAM Journal on Control, Vol. 3, No. 1, 1965.

  14. Fleming, W. H.,The Convergence Problem for Differential Games, Journal of Mathematical Analysis and Applications, Vol. 3, No. 1, 1961.

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by L. Cesari

Rights and permissions

Reprints and permissions

About this article

Cite this article

Roxin, E. Axiomatic approach in differential games. J Optim Theory Appl 3, 153–163 (1969). https://doi.org/10.1007/BF00929440

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00929440

Keywords

Navigation