Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.20826 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916339570966528 |
|---|---|
| author | Ignazio, Vincenzo Ricciardi, Michele |
| author_facet | Ignazio, Vincenzo Ricciardi, Michele |
| contents | Mean Field Games (MFG) theory describes strategic interactions in differential games with a large number of small and indistinguishable players. Traditionally, the players' control impacts only the drift term in the system's dynamics, leaving the diffusion term uncontrolled. This paper explores a novel scenario where agents control both drift and diffusion. This leads to a fully non-linear MFG system with a fully non-linear Hamilton-Jacobi-Bellman equation. We use viscosity arguments to prove existence of solutions for the HJB equation, and then we adapt and extend a result from Krylov to prove a $\mathcal C^3$ regularity for $u$ in the space variable. This allows us to prove a well-posedness result for the MFG system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20826 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A second-order Mean Field Games model with controlled diffusion Ignazio, Vincenzo Ricciardi, Michele Analysis of PDEs Mean Field Games (MFG) theory describes strategic interactions in differential games with a large number of small and indistinguishable players. Traditionally, the players' control impacts only the drift term in the system's dynamics, leaving the diffusion term uncontrolled. This paper explores a novel scenario where agents control both drift and diffusion. This leads to a fully non-linear MFG system with a fully non-linear Hamilton-Jacobi-Bellman equation. We use viscosity arguments to prove existence of solutions for the HJB equation, and then we adapt and extend a result from Krylov to prove a $\mathcal C^3$ regularity for $u$ in the space variable. This allows us to prove a well-posedness result for the MFG system. |
| title | A second-order Mean Field Games model with controlled diffusion |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2407.20826 |