Some Problems in Optimal Visiting Mean Field Games: Continuity Equation with Sinks and Switching Representation on a Network
With Fabio Bagagiolo, Università degli Studi di Trento.
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An optimal visiting problem consists in touching some targets (regions of R^n) along the controlled trajectory, optimizing a suitable cost. The associated mean field game corresponds to the case where a huge population of agents perform the same optimal visiting problem and the costs also depend on the congestion. The population is then dynamically split into several populations labelled by the targets that have been already visited. There is therefore a transfer between the sub-populations and the continuity equation presents some sink-terms. The labels may also be interpreted as nodes of a direct network, giving a switching dynamics on it.