Feedback and open-loop Nash equilibria in a class of differential games with random duration
Contributions to game theory and management, Tome 13 (2020), pp. 415-426.

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One class of differential games with random duration is considered. It is assumed that duration of the game is a random variable with values from a given finite interval. The game can be interrupted only on this interval. Methods of construction feedback and open-loop Nash equilibria for such games are proposed.
Keywords: differential game, Nash equilibrium, random variable, open-loop strategies, feedback strategies.
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Anna V. Tur; Natalya G. Magnitskaya. Feedback and open-loop Nash equilibria in a class of differential games with random duration. Contributions to game theory and management, Tome 13 (2020), pp. 415-426. http://geodesic.mathdoc.fr/item/CGTM_2020_13_a22/

[1] Başar T., Olsder G., Dynamic Non-Cooperative Game Theory, Academic Press, London, 1995 | MR

[2] Dockner E. J., S. Jorgensen, N. van Long, G. Sorger, Differential Games in Economics and Management Science, Cambridge Univ. Press, 2000 | MR | Zbl

[3] Gromov D., Gromova E., “On a Class of Hybrid Differential Games”, Dyn. Games Appl., 7 (2017), 266–288 | DOI | MR | Zbl

[4] Gromova E. V., Magnitskaya N. G., “Solution of the differential game with hybrid structure”, Contributions to Game Theory and Management, 12 (2019), 159–176 | MR

[5] Gromova E., Tur A., “On the form of integral payoff in differential games with random duration”, 2017 XXVI International Conference on Information, Communication and Automation Technologies (ICAT) (Sarajevo, 2017), 2017, 1–6 | DOI

[6] Petrosyan L. A., Murzov N. V., “Game-theoretic Problems in Mechanics”, Lithuanian Mathematical Collection, 3 (1966), 423–433 | DOI | MR

[7] Petrosyan L. A., Shevkoplyas E. V., “Cooperative differential games with random duration”, Vestnik Sankt-Peterburgskogo Universiteta. Ser 1. Matematika Mekhanika Astronomiya, 2000, no. 4, 18–23 | MR | Zbl

[8] Pontryagin L. S., V. G. Boltyanskii, R. V. Gamkrelidze, E. F. Mishchenko, The Mathematical Theory of Optimal Processes, Wiley-Interscience, 1963 | MR

[9] Shevkoplyas E. V., “The Hamilton-Jacobi-Bellman equation for a class of differential games with random duration”, Autom. Remote Control, 75 (2014), 959–970 | DOI | MR