Ergodic McKean-Vlasov Games: Verification Theorems and Linear-Quadratic Applications
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915851400118272 |
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| author | Song, Qingshuo Wang, Gu Xu, Zuo Quan Zhu, Chao |
| author_facet | Song, Qingshuo Wang, Gu Xu, Zuo Quan Zhu, Chao |
| contents | This paper investigates two-player ergodic nonzero-sum stochastic differential games with McKean-Vlasov dynamics. We establish a verification theorem connecting solutions of coupled Hamilton-Jacobi-Bellman (HJB) Master equations to Nash equilibria, characterized through an auxiliary control problem defined on the measure space. A key contribution is showing that the value functions are uniquely determined (up to an additive constant) by the uniqueness of the invariant measure of the optimal state process. The theory is applied to Linear-Quadratic-Gaussian (LQG) settings, where explicit solutions to the Master equations are derived by exploiting their polynomial structure in measure variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01972 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ergodic McKean-Vlasov Games: Verification Theorems and Linear-Quadratic Applications Song, Qingshuo Wang, Gu Xu, Zuo Quan Zhu, Chao Optimization and Control 93E20, 91A15, 91A23 This paper investigates two-player ergodic nonzero-sum stochastic differential games with McKean-Vlasov dynamics. We establish a verification theorem connecting solutions of coupled Hamilton-Jacobi-Bellman (HJB) Master equations to Nash equilibria, characterized through an auxiliary control problem defined on the measure space. A key contribution is showing that the value functions are uniquely determined (up to an additive constant) by the uniqueness of the invariant measure of the optimal state process. The theory is applied to Linear-Quadratic-Gaussian (LQG) settings, where explicit solutions to the Master equations are derived by exploiting their polynomial structure in measure variables. |
| title | Ergodic McKean-Vlasov Games: Verification Theorems and Linear-Quadratic Applications |
| topic | Optimization and Control 93E20, 91A15, 91A23 |
| url | https://arxiv.org/abs/2505.01972 |