Geodesic
Feedback based strategies for autonomous linear quadratic cooperative differential games with continuous updating
Contributions to game theory and management, Tome 13 (2020), pp. 244-251.

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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, differential games with continuous updating. 
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     author = {Ildus Kuchkarov},
     title = {Feedback based strategies for autonomous linear quadratic cooperative differential games with continuous updating},
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     volume = {13},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2020_13_a12/}
}
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Ildus Kuchkarov. Feedback based strategies for autonomous linear quadratic cooperative differential games with continuous updating. Contributions to game theory and management, Tome 13 (2020), pp. 244-251. http://geodesic.mathdoc.fr/item/CGTM_2020_13_a12/

[1] Basar T., G. Olsder, Dynamic noncooperative game theory, Academic Press, London, 1995 | MR | Zbl

[2] Bellman R., Dynamic Programming, Princeton University Press, Princeton, 1957 | MR | Zbl

[3] Engwerda J., LQ Dynamic Optimization and Differential Games, Willey, New York, 2005

[4] Kleimenov A., Non-antagonistic positional differential games, Science, Ekaterinburg, 1993 | MR

[5] Kuchkarov I., O. Petrosian, “On Class of Linear Quadratic Non-cooperative Differential Games with Continuous Updating”, Mathematical Optimization Theory and Operations Research, MOTOR 2019, Lecture Notes in Computer Science, 11548, eds. Khachay M., Y. Kochetov, P. Pardalos, Springer, Cham, 2019, 635–650 | DOI | MR | Zbl

[6] Petrosian O. L., “Looking Forward Approach in Cooperative Differential Games”, International Game Theory Review, 18:2 (2016), 1–14 | MR

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

[8] Petrosian O., A. Tur, “Hamilton-Jacobi-Bellman Equations for Non-cooperative Differential Games with Continuous Updating”, Mathematical Optimization Theory and Operations Research, MOTOR 2019, Communications in Computer and Information Science, 1090, eds. Bykadorov I., V. Strusevich, T. Tchemisov, Springer, Cham, 2019, 178–191 | DOI | MR

[9] Petrosyan L., N. Murzov, “Game-theoretic problems in mechanics”, Lithuanian Mathematical Collection, 3 (1966), 423–433 | DOI | MR

[10] Pontryagin L., “On the theory of differential games”, Successes of Mathematical Sciences, 4(130) (1966), 219–274 | MR | Zbl

[11] Shevkoplyas E., “Optimal solutions in differential games with random duration”, Journal of Mathematical Sciences, 199:6 (2014), 715–722 | DOI | MR | Zbl