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This document discusses first-order stationary mean-field games (MFGs) with congestion, focusing on the challenges of finding classical solutions and the existence of areas with vanishing densities. The authors introduce a new variational formulation for MFGs with congestion, proving the existence and uniqueness of solutions, and explore its applications to numerical methods. The paper also addresses the critical difficulties in analyzing first-order Hamilton–Jacobi equations and presents explicit examples

Author

prashantkhattri14

Language

EN