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Convergence of some mean field games systems to aggregation and flocking models. (English) Zbl 1460.35349
The authors investigate the convergence of solutions for two classes of Mean Field Game (MFG) systems. The first class of MFG systems with control on the velocity is given by a parabolic system with a large parameter \(\lambda\) associated to a stochastic MFG, for which the solution converges to a solution of a aggregation model as \(\lambda\to\infty\). The second class of MFG systems with control on acceleration is a first order PDEs system for which the solution converges to the solution of a kinetic equation. In the main results, they use PDEs methods for the first model, and variational methods in the space of probability measures on trajectories for the second model.
MSC:
35Q89 PDEs in connection with mean field game theory
91A16 Mean field games (aspects of game theory)
35R09 Integral partial differential equations
45K05 Integro-partial differential equations
93C20 Control/observation systems governed by partial differential equations
Software:
Matlab
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