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Decision-making in a hybrid two-step problem of dynamic control
Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 123, pp. 415-423 Cet article a éte moissonné depuis la source Math-Net.Ru

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The equations of motion of the controlled system in the two-step problem under consideration at a fixed time interval contain the controls of either one player or two players. In the first step (stage) of the controlled process (from the initial moment to a certain predetermined moment), only the first player controls the system, which solves the problem of optimal control with a given terminal functional. In the second step (stage) of the process, the first player decides whether the second player will participate in the control process for the remainder of the time, or not. It is assumed that for participation the second player must pay the first side payment in a fixed amount. If «yes», then a non-antagonistic positional differential game is played out, in which the Nash equilibrium is taken as the solution. In addition, players can use «abnormal» behaviors, which can allow players to increase their winnings. If «no», then until the end of the process continues to solve the problem optimal control.
Keywords: optimal control problem, non-antagonistic positional differential game, Nash equilibrium, players’ behavior types. 
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A. F. Kleimenov. Decision-making in a hybrid two-step problem of dynamic control. Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 123, pp. 415-423. http://geodesic.mathdoc.fr/item/VTAMU_2018_23_123_a8/

[1] L. A. Petrosyan, N. A. Zenkevich, E. V. Shevkoplyas, Game Theory, BKHV-Peterburg Publ., St. Petersburg, 2012 (In Russian)

[2] P. M. Kort, S. Wrzaczek, “Optimal firm growth under the threat of entry”, Eur. J. Oper. Res., 246:1 (2015), 281–292 | DOI | MR

[3] N. N. Krasovskiy, A. I. Subbotin, Positional Differentional Games, Nauka Publ., Moscow, 1974, 456 pp. (In Russian) | MR

[4] N. N. Krasovskiy, Control of a Dynamic System, Nauka Publ., Moscow, 1985 (In Russian)

[5] A. F. Kleymenov, Nonantagonistic Positional Differential Games, Nauka Publ., Yekaterinburg, 1993 (In Russian)

[6] A. F. Kleymenov, “On solutions in a nonantagonistic positional differential game”, Journal of Applied Mathematics and Mechanics, 61:5 (1997), 739–746 (In Russian) | MR

[7] A. F. Kleimenov, A. V. Kryazhimskii, Normal Behavior, Altruism and Aggression in Cooperative Game Dynamics, Interim Report IR-98-076, IIASA, Laxenburg, 1998, 47 pp.

[8] A. F. Kleimenov, “An Approach to Building Dynamics for Repeated Bimatrix $2\times2$ Games Involving Various Behavior Types”, Dynamic and Control, ed. G. Leitman (ed.), Gordon and Breach, London, 1998, 195–204 | MR

[9] A. F. Kleymenov, “Altruistic behavior in a non-antagonistic positional differential game”, Mathematical Theory of Games and Its Applications, 7:4 (2015), 40–55 (In Russian) | MR

[10] A. F. Kleymenov, “Application of the altruistic and aggressive types of behavior in a two-person non-zero-sum positional differential game on the plane”, Proceedings of the Steklov Institute of Mathematics, 23, no. 4, 2017, 181–191 (In Russian)