Robustness and Approximation of Discrete-time Mean-field Games under Discounted Cost Criterion
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911577556385792 |
|---|---|
| author | Aydın, Uğur Saldi, Naci |
| author_facet | Aydın, Uğur Saldi, Naci |
| contents | In this paper, we investigate the robustness of stationary mean-field equilibria in the presence of model uncertainties, specifically focusing on infinite-horizon discounted cost functions. To achieve this, we initially establish convergence conditions for value iteration-based algorithms in mean-field games. Subsequently, utilizing these results, we demonstrate that the mean-field equilibrium obtained through this value iteration algorithm remains robust even in the face of system dynamics misspecifications. We then apply these robustness findings to the finite model approximation problem in mean-field games, showing that if the state space quantization is fine enough, the mean-field equilibrium for the finite model closely approximates the nominal one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_10828 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Robustness and Approximation of Discrete-time Mean-field Games under Discounted Cost Criterion Aydın, Uğur Saldi, Naci Systems and Control Optimization and Control In this paper, we investigate the robustness of stationary mean-field equilibria in the presence of model uncertainties, specifically focusing on infinite-horizon discounted cost functions. To achieve this, we initially establish convergence conditions for value iteration-based algorithms in mean-field games. Subsequently, utilizing these results, we demonstrate that the mean-field equilibrium obtained through this value iteration algorithm remains robust even in the face of system dynamics misspecifications. We then apply these robustness findings to the finite model approximation problem in mean-field games, showing that if the state space quantization is fine enough, the mean-field equilibrium for the finite model closely approximates the nominal one. |
| title | Robustness and Approximation of Discrete-time Mean-field Games under Discounted Cost Criterion |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2310.10828 |