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Intro; Preface; Contents; About the Editors; Uniqueness of Solutions in Mean Field Games with Several Populations and Neumann Conditions; 1 Introduction; 2 The Uniqueness Theorem; 2.1 The Main Result; 2.2 Examples and Remarks; 3 Special Cases and Applications; 3.1 Well-Posedness of Segregation Models; 3.2 Well-Posedness of Robust Mean Field Games; Appendix: A Comparison Principle; References; Finite Difference Methods for Mean Field Games Systems; 1 Introduction; 2 A Finite Difference Scheme for Mean Field Games on the Torus; 2.1 Convergence for V Nonlocal Operator
2.2 Convergence for V Local Operator3 Mean Field Games on Networks; 3.1 Networks and Functional Spaces; 3.2 A Formal Derivation of the MFG System on a Network; 3.3 A Finite Difference Scheme for Mean Field Games on Networks; 3.4 Existence, Uniqueness and Convergence of the Numerical Scheme; 4 A Quasi-Newton Method for Stationary Mean Field Games; 4.1 MFG in Euclidean Spaces; 4.2 Multi-Population MFG in Euclidean Spaces; 4.3 MFG on Networks; References; Existence and Uniqueness for Mean Field Games with StateConstraints; 1 Introduction; 2 Preliminaries; 2.1 Notation
2.2 Results from Measure Theory3 Constrained MFG Equilibria; 3.1 Approximation of Constrained Trajectories; 3.2 Assumptions; 3.3 Existence of Constrained MFG Equilibria; 3.4 Proof of Theorem 3.1; 4 Mild Solution of the Constrained MFG Problem; References; An Adjoint-Based Approach for a Class of Nonlinear Fokker-Planck Equations and Related Systems; 1 Introduction; 2 Adjoint Structure; 2.1 Linearization and Duality; 2.2 Boundary Conditions; 3 Properties; 4 Numerical Approach; 4.1 Finite Differences; 4.2 Semi-Lagrangian Scheme; 5 Applications to Systems of PDEs
5.1 Example: Hughes Model in 1-D5.2 Example: 1-D Forward-Forward Mean-Field Games; 5.3 Example: Hughes Model in 2-D; 6 Conclusions; References; Variational Mean Field Games for Market Competition; 1 Introduction; 1.1 Explanation of the Model; 1.2 Notation and Assumptions; 2 Analysis of the System; 2.1 Uniqueness Revisited for the Model of Chan and Sircar; 3 Optimal Control of Fokker-Planck Equation; 4 First-Order Case; References; A Review for an Isotropic Landau Model; 1 Introduction; 1.1 The Isotropic Landau Equation; 1.2 Conserved Quantities and Entropy Structure
2.2 Convergence for V Local Operator3 Mean Field Games on Networks; 3.1 Networks and Functional Spaces; 3.2 A Formal Derivation of the MFG System on a Network; 3.3 A Finite Difference Scheme for Mean Field Games on Networks; 3.4 Existence, Uniqueness and Convergence of the Numerical Scheme; 4 A Quasi-Newton Method for Stationary Mean Field Games; 4.1 MFG in Euclidean Spaces; 4.2 Multi-Population MFG in Euclidean Spaces; 4.3 MFG on Networks; References; Existence and Uniqueness for Mean Field Games with StateConstraints; 1 Introduction; 2 Preliminaries; 2.1 Notation
2.2 Results from Measure Theory3 Constrained MFG Equilibria; 3.1 Approximation of Constrained Trajectories; 3.2 Assumptions; 3.3 Existence of Constrained MFG Equilibria; 3.4 Proof of Theorem 3.1; 4 Mild Solution of the Constrained MFG Problem; References; An Adjoint-Based Approach for a Class of Nonlinear Fokker-Planck Equations and Related Systems; 1 Introduction; 2 Adjoint Structure; 2.1 Linearization and Duality; 2.2 Boundary Conditions; 3 Properties; 4 Numerical Approach; 4.1 Finite Differences; 4.2 Semi-Lagrangian Scheme; 5 Applications to Systems of PDEs
5.1 Example: Hughes Model in 1-D5.2 Example: 1-D Forward-Forward Mean-Field Games; 5.3 Example: Hughes Model in 2-D; 6 Conclusions; References; Variational Mean Field Games for Market Competition; 1 Introduction; 1.1 Explanation of the Model; 1.2 Notation and Assumptions; 2 Analysis of the System; 2.1 Uniqueness Revisited for the Model of Chan and Sircar; 3 Optimal Control of Fokker-Planck Equation; 4 First-Order Case; References; A Review for an Isotropic Landau Model; 1 Introduction; 1.1 The Isotropic Landau Equation; 1.2 Conserved Quantities and Entropy Structure