Abstract
In this paper, we consider a zero-sum differential game that can be stopped by any of the participants at one of time points known in advance. The cost functional may depend both on the time when the game ends and the position of the system at that time and on the player who initiates the game stopping. When optimizing the expectation of this functional, each player, based on the information the player has about the realized trajectory of the system, makes decisions both about his/her probability of stopping the game and about his/her own control of the conflict-controlled system; however, nondeterministic distribution rules are also allowed. The existence of the game value is shown under the assumption of a saddle point condition in the small game (the Isaacs condition). The construction of a stochastic guide whose model is a continuous-time Markov chain was used to construct approximately optimal strategies for the players.
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This work was supported by the Russian Science Foundation, project no. 17-11-01093.
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Translated by V. Potapchouck
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Khlopin, D.V. Differential Game with Discrete Stopping Time. Autom Remote Control 83, 649–672 (2022). https://doi.org/10.1134/S0005117922040105
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DOI: https://doi.org/10.1134/S0005117922040105