Skip to main content
Log in

Sufficient conditions for optimality of threat strategies in a differential game

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

Abstract

The problem of defining threat strategies in nonzero-sum games is considered, and a definition of optimal threat strategies is proposed in the static case. This definition is then extended to differential games, and sufficient conditions for optimality of threat strategies are derived. These are then applied to a simple example. The definition proposed here is then compared with the definition of threat strategies given by Nash.

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. Nash, J. P.,Two-Person Cooperative Games, Econometrica, Vol. 21, pp. 128–140, 1953.

    Google Scholar 

  2. Liu, P. T.,Optimal Threat Strategies in Differential Games, Journal of Mathematical Analysis and Applications, Vol. 43, No. 1, 1973.

  3. Blaquiere, A.,Necessary and Sufficiency Conditions for Optimal Strategies in Impulsive Control, Differential Games and Control Theory, III, Edited by P. T. Liu and E. Roxin, Marcel Dekker, New York, New York, 1979.

    Google Scholar 

  4. Leitmann, G.,Cooperative and Noncooperative Differential Games, Multicriteria Decision Making, Edited by G. Leitmann and A. Marzollo, Springer-Verlag, New York, New York, 1975.

    Google Scholar 

  5. Blaquiere, A., Juricek, L., andWiese, K. E.,Geometry of Pareto Equilibria in N-Person Differential Games, Journal of Mathematical Analysis and Applications, Vol. 38, No. 1, 1972.

  6. Blaquiere, A., Gerard, F., andLeitmann, G.,Quantitative and Qualitative Games, Academic Press, New York, New York, 1969.

    Google Scholar 

  7. Liu, P. T.,Nonzero-Sum Differential Games with Bargaining Solutions, Journal of Optimization Theory and Applications, Vol. 11, No. 3, 1973.

  8. Leitmann, G.,Sufficiency Theorems for Optimal Control, Journal of Optimization Theory and Applications, Vol. 2, No. 5, 1968.

  9. Leitmann, G.,A Note on a Sufficiency Theorem for Optimal Control, Journal of Optimization Theory and Applications, Vol. 3, No. 1, 1969.

  10. Leitmann, G., andSchmitendorf, W.,Some Sufficient Conditions for Pareto-Optimal Control, Journal of Dynamical Systems, Measurement, and Control, Vol. 95, No. 4, 1973.

  11. Wang, G., andLeitmann, G.,Necessary and Sufficient Conditions for Multi-Stage Two-Person Zero-Sum Games, Journal of Optimization Theory and Applications, Vol. 4, No. 3, 1969.

  12. Stalford, H., andLeitmann, G.,On Integrals of a Class of Measurable Functions, Journal of the Franklin Institute, Vol. 290, No. 2, 1970.

  13. Stalford, H., andLeitmann, G.,Sufficient Conditions for Optimality in Two-Person, Zero-Sum Differential Games with State and Strategy Constraints, Journal of Mathematical Analysis and Applications, Vol. 33, No. 3, 1971.

  14. Stalford, H., andLeitmann, G.,Sufficient Conditions for Nash Equilibria in N-Person Differential Games, Topics in Differential Games, Edited by A. Blaquière, North-Holland Publishing Company, Amsterdam, Holland, 1973.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by G. Leitmann

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ray, A., Blaquière, A. Sufficient conditions for optimality of threat strategies in a differential game. J Optim Theory Appl 33, 99–109 (1981). https://doi.org/10.1007/BF00935179

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00935179

Key Words

Navigation