Skip to main content

Closed-loop stackelberg solution and threats in dynamic games

  • Differential Games
  • Conference paper
  • First Online:
Optimization Techniques

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 22))

Abstract

A solution of the deterministic two-person closed-loop Stackelberg game with linear dynamics and quadratic cost functions has been discussed, with the emphasis made on interpretation of the proposed Stackelberg strategies. The basic result has been formulated for the game with the leader perfectly dominating the follower, and then various extensions of this result for more general games have been outlined. It should be noted, that although a considerable progress in the study of closed-loop Stackelberg games has recently been achieved, many aspects of the theory, especially those concerned with continuous-time and multiperson problems, require further investigation.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Basar T., Selbuz H., A new Approach for Derivation of Closed-Loop Stackelberg Strategies. Proc. IEEE Conf. on Decision and Control, San Diego (Jan. 1979).

    Google Scholar 

  2. Basar T., Selbuz H., Closed-loop Stackelberg Strategies with Applications in the Optimal Control of Multi-level Systems. IEEE Trans. on Automatic Control vol.AC-24: 1979 No.2.

    Google Scholar 

  3. Basar T., Olsder G.J., Team-optimal Closed-loop Stackelberg Strategies in Hierarchical Control Problems. Memo. No. 242, Twente Univ. of Technology, 1979 r.

    Google Scholar 

  4. Chen C.I., Cruz J.B. Jr., Stackelberg Solution for Two-Person Games with Biased Information Patterns. IEEE Trans. on Automatic Control vol. AC-17: 1972 No.6

    Google Scholar 

  5. Kwakernaak H., Sivan R., Linear Optimal Control Systems. New York: Wiley-Interscience 1972.

    Google Scholar 

  6. Papavassilopoulos G.P., Cruz J.B.Jr., Sufficient Conditions for Stackelberg and Nash Strategies with Memory. J. Optimiz. Theory a. Applications to appear.

    Google Scholar 

  7. Tołwiński B., Closed-loop Stackelberg Solution to Multistage Linear-Quadratic Game. Systems Research Institute, Report ZTSW-64/79, March 1979 r.

    Google Scholar 

  8. Tołwiński B., Closed-Loop Stackelberg Solution to Multistage Linear-Quadratic Game. J. Optimiz. Theory a. Applications (to appear).

    Google Scholar 

  9. Tołwiński B., Closed-loop Stackelberg Strategies for Differential Games. Systems Research Institute, Report ZTSW-64/79, June 1979 r.

    Google Scholar 

  10. Tołwiński B., Information and Dominant Player Solutions in Linear-Quadratic Dynamic Games. Systems Research Institute, Report ZTSW-64/79, September 1979.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

K. Iracki K. Malanowski S. Walukiewicz

Rights and permissions

Reprints and permissions

Copyright information

© 1980 Springer-Verlag

About this paper

Cite this paper

Tołwiński, B. (1980). Closed-loop stackelberg solution and threats in dynamic games. In: Iracki, K., Malanowski, K., Walukiewicz, S. (eds) Optimization Techniques. Lecture Notes in Control and Information Sciences, vol 22. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0036401

Download citation

  • DOI: https://doi.org/10.1007/BFb0036401

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10080-5

  • Online ISBN: 978-3-540-38248-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics