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Explore a comprehensive lecture on mean-field games (MFGs) using monotonicity techniques. Delve into the study of MFGs as the limit of differential games with large populations. Examine the structure of MFG models, comprising Hamilton-Jacobi and Fokker-Planck equations associated with monotone operators. Understand how this structure is crucial for establishing solution uniqueness. Investigate the challenges in proving existence of solutions for MFGs, focusing on the complexities arising from the coupling of equations. Learn how monotone operator concepts provide a unified approach to address weak solution existence for various MFG classes, including stationary problems with periodic or Dirichlet boundary conditions, time-dependent problems, and planning problems with congestion.
