Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.02244 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918180721524736 |
|---|---|
| author | Tangpi, Ludovic Wang, Shichun |
| author_facet | Tangpi, Ludovic Wang, Shichun |
| contents | We present a simpler proof of the existence of equilibria for a class of mean field games with common noise, where players interact through the conditional law given the current value of the common noise rather than its entire path. By extending a compactness criterion for Malliavin-differentiable random variables to processes, we establish existence of strong equilibria, where the conditional law and optimal control are adapted to the common noise filtration and defined on the original probability space. Notably, our approach only requires measurability of the drift and cost functionals with respect to the state variable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02244 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mean field games with common noise via Malliavin calculus Tangpi, Ludovic Wang, Shichun Probability 91A16, 60H07 We present a simpler proof of the existence of equilibria for a class of mean field games with common noise, where players interact through the conditional law given the current value of the common noise rather than its entire path. By extending a compactness criterion for Malliavin-differentiable random variables to processes, we establish existence of strong equilibria, where the conditional law and optimal control are adapted to the common noise filtration and defined on the original probability space. Notably, our approach only requires measurability of the drift and cost functionals with respect to the state variable. |
| title | Mean field games with common noise via Malliavin calculus |
| topic | Probability 91A16, 60H07 |
| url | https://arxiv.org/abs/2405.02244 |