Abstract
We introduce a bilevel problem of the optimal control of an interacting agent system that can be interpreted as Stackelberg game with a large number of followers. It is shown that the model is well posed by providing conditions that allow to formally reduce the problem to a single level unconstrained problem. The mean-field limit is derived formally for infinitely many followers at three different stages of the optimization and the commutativity of these operations (the mean-field limit and first-order optimality on leader and on follower level) is studied. Further, we establish conditions for consistency for the relation between bilevel optimization and mean-field limit. Finally, we propose a numerical method based on the derived models and present numerical examples.
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