Mean Field Games for Modeling Crowd Motion
We present a model for crowd motion based on the recent theory of mean field games. The model takes congestion effects into account. A robust and efficient numerical method is discussed. Numerical simulations are presented for two examples. The second example, in which all the agents share a common source of risk and have incomplete information, is of particular interest, because it cannot be dealt with without modeling rational anticipation.
The first author would like to affectionately dedicate this work to Yuri Kuznetsov and Olivier Pironneau for their seventieth birthdays. The first author was partially funded by the ANR projects ANR-12-MONU-0013 and ANR-12-BS01-0008-01. The two authors acknowledge the support of the Chaire “Finance et développement durable”.
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