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A Unifying Framework for Submodular Mean Field Games2. A general approach to submodular MFGs2.3. Existence and approximation of MFG solutions

1. Introduction

1.1. Existence and approximation results in MFGs
1.2. Examples.
1.3. Outline of the paper

General notation
2. A general approach to submodular MFGs

2.1. Formulation of the abstract model
2.2. Submodularity conditions and properties of the best-response-map
2.3. Existence and approximation of MFG solutions

3. Lattices of measures related to submodular MFG
4. Submodular mean field games with Markov chains
5. Submodular mean field games with singular controls

5.1. Controlled geometric Brownian motion and common noise
5.2. Nonconvex case without common noise
5.3. Remarks and extensions

6. Submodular mean field games with reflecting boundary conditions

6.1. Formulation of the model
6.2. Reformulation via control rules and preliminary results
6.3. Existence and approximation of equilibria

7. Supermodular mean field games with optimal stopping

7.1. Formulation of the model
7.2. Reformulation and preliminary results
7.3. Existence and approximation of equilibria
7.4. Comments and examples

Appendix A. Lattice-theoretic preliminaries
References

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A Unifying Framework for Submodular Mean Field Games

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