Dianetti, Jodi; Ferrari, Giorgio; Fischer, Markus; Nendel, Max: A Unifying Framework for Submodular Mean Field Games. In: . Jg.661. 2022, S. 37 ff.
Inhalt
- 1. Introduction
- 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