Feedback Based Strategies for Autonomous Linear Quadratic Cooperative Differential Games with Continuous Updating

Authors

  • Ildus Kuchkarov Saint Petersburg State University

DOI:

https://doi.org/10.21638/11701/spbu31.2020.13

Abstract

In the paper the class of linear quadratic cooperative differential games with continuous updating is considered. Here the case of feedback based strategies is used to construct cooperative strategies with continuous updating. Characteristic function with continuous updating, cooperative trajectory with continuous updating and cooperative solution are constructed. For the cooperative solution we use the Shapley value.

Keywords:

cooperative differential games, differential games with continuous updating

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References

Basar, T. and G. Olsder (1995). Dynamic noncooperative game theory. Academic Press: London

Bellman, R. (1957). Dynamic Programming. Princeton University Press: Princeton

Engwerda, J. (2005). LQ Dynamic Optimization and Differential Games. Willey: New York

Kleimenov, A. (1993). Non-antagonistic positional differential games. Science: Ekaterinburg

Kuchkarov, I. and O. Petrosian (2019). On Class of Linear Quadratic Non-cooperative Differential Games with Continuous Updating. In: Mathematical Optimization Theory and Operations Research. MOTOR 2019. Lecture Notes in Computer Science (Khachay, M., Y. Kochetov, P. Pardalos eds) Lecture Notes in Computer Science, Vol. 11548, 635–650. Springer: Cham

Petrosian, O. L. (2016). Looking Forward Approach in Cooperative Differential Games. International Game Theory Review, 18(2), 1–14

Petrosian, O. L. (2016). Looking Forward Approach in Cooperative Differential Games with infinite-horizon. Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 4, 18–30

Petrosian, O. and A. Tur (2019). Hamilton-Jacobi-Bellman Equations for Non-cooperative Differential Games with Continuous Updating. In: Mathematical Optimization Theory and Operations Research. MOTOR 2019. Communications in Computer and Information Science (Bykadorov, I., V. Strusevich, T. Tchemisova eds.), Vol. 1090, 178–191. Springer: Cham

Petrosyan, L. and N. Murzov (1966). Game-theoretic problems in mechanics. Lithuanian Mathematical Collection, 3, 423–433

Pontryagin, L. (1966). On the theory of differential games. Successes of Mathematical Sciences, 4(130), 219–274

Shevkoplyas, E. (2014). Optimal solutions in differential games with random duration. Journal of Mathematical Sciences, 199(6), 715–722

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Published

2022-02-02

How to Cite

Kuchkarov, I. (2022). Feedback Based Strategies for Autonomous Linear Quadratic Cooperative Differential Games with Continuous Updating. Contributions to Game Theory and Management, 13. https://doi.org/10.21638/11701/spbu31.2020.13

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Articles