New Uniqueness Results For A Mean Field Game Of Controls
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909353975480320 |
|---|---|
| author | Graber, Jameson Matter, Elizabeth |
| author_facet | Graber, Jameson Matter, Elizabeth |
| contents | We propose a new approach to proving the uniqueness of solutions to a certain class of mean field games of controls. In this class, the equilibrium is determined by an aggregate quantity $Q(t)$, e.g. the market price or production, which then determines optimal trajectories for agents. Our approach consists in analyzing the relationship between $Q(t)$ and corresponding optimal trajectories to find conditions under which there is at most one equilibrium. We show that our conditions do not match those prescribed by the Lasry-Lions monotonicity condition, nor even displacement monotonicity, but they do apply to economic models that have been proposed in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_13950 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New Uniqueness Results For A Mean Field Game Of Controls Graber, Jameson Matter, Elizabeth Optimization and Control Analysis of PDEs 49N80(Primary), 35Q89(Secondary) We propose a new approach to proving the uniqueness of solutions to a certain class of mean field games of controls. In this class, the equilibrium is determined by an aggregate quantity $Q(t)$, e.g. the market price or production, which then determines optimal trajectories for agents. Our approach consists in analyzing the relationship between $Q(t)$ and corresponding optimal trajectories to find conditions under which there is at most one equilibrium. We show that our conditions do not match those prescribed by the Lasry-Lions monotonicity condition, nor even displacement monotonicity, but they do apply to economic models that have been proposed in the literature. |
| title | New Uniqueness Results For A Mean Field Game Of Controls |
| topic | Optimization and Control Analysis of PDEs 49N80(Primary), 35Q89(Secondary) |
| url | https://arxiv.org/abs/2410.13950 |