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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