Abstract
The paper deals with game-theoretical control problem for the continuity equation. It is assumed that all agents of a multiagent system are influenced by the same controls of both players depending only on current time and current distribution of the agents. We extend the notion of \(u\)- and \(v\)-stability and the Krasovskii–Subbotin extremal shift rule to a given case and construct suboptimal strategies of players. Also, the existence theorem for a value function is proved.
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Acknowledgments
The author wishes to express gratitude to Dr. of Mathematics Yu. V. Averboukh for his valuable comments.
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Translated from Matematicheskie Zametki, 2023, Vol. 114, pp. 525–542 https://doi.org/10.4213/mzm13898.
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Kolpakova, E.A. Feedback Strategies in a Game-Theoretical Control Problem for a Nonlocal Continuity Equation. Math Notes 114, 457–471 (2023). https://doi.org/10.1134/S0001434623090183
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DOI: https://doi.org/10.1134/S0001434623090183