Linear-quadratic stochastic nonzero-sum differential games between graphon teams
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913891056877568 |
|---|---|
| author | Xu, De-xuan Gou, Zhun Huang, Nan-jing |
| author_facet | Xu, De-xuan Gou, Zhun Huang, Nan-jing |
| contents | We study a class of nonzero-sum stochastic differential games between two teams with agents in each team interacting through graphon aggregates. On the one hand, in each large population group, agents act together to optimize a common social cost function. On the other hand, these two groups compete with each other, forming a Nash game between two graphon teams. We note that the original problem can be equivalently formulated as an infinite-dimensional two-agent Nash game. Applying the dynamic programming approach, we obtain a set of coupled operator-valued Riccati-type equations. By proving the existence of solutions to the equations mentioned above, we obtain a Nash equilibrium for the two teams. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11468 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear-quadratic stochastic nonzero-sum differential games between graphon teams Xu, De-xuan Gou, Zhun Huang, Nan-jing Optimization and Control We study a class of nonzero-sum stochastic differential games between two teams with agents in each team interacting through graphon aggregates. On the one hand, in each large population group, agents act together to optimize a common social cost function. On the other hand, these two groups compete with each other, forming a Nash game between two graphon teams. We note that the original problem can be equivalently formulated as an infinite-dimensional two-agent Nash game. Applying the dynamic programming approach, we obtain a set of coupled operator-valued Riccati-type equations. By proving the existence of solutions to the equations mentioned above, we obtain a Nash equilibrium for the two teams. |
| title | Linear-quadratic stochastic nonzero-sum differential games between graphon teams |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2506.11468 |