Long-Time Behavior of Zero-Sum Linear-Quadratic Stochastic Differential Games
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916273313546240 |
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| author | Sun, Jingrui Yong, Jiongmin |
| author_facet | Sun, Jingrui Yong, Jiongmin |
| contents | The paper investigates the long-time behavior of zero-sum linear-quadratic stochastic differential games, aiming to demonstrate that, under appropriate conditions, both the saddle strategy and the optimal state process exhibit the exponential turnpike property. Namely, for the majority of the time horizon, the distributions of the saddle strategy and the optimal state process closely stay near certain (time-invariant) distributions $ν_1^*$, $ν_2^*$ and $μ^*$, respectively. Additionally, as a byproduct, we solve the infinite horizon version of the differential game and derive closed-loop representations for its open-loop saddle strategy, which has not been proved in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02089 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Long-Time Behavior of Zero-Sum Linear-Quadratic Stochastic Differential Games Sun, Jingrui Yong, Jiongmin Optimization and Control 91A05, 91A15, 49N10, 49N70 The paper investigates the long-time behavior of zero-sum linear-quadratic stochastic differential games, aiming to demonstrate that, under appropriate conditions, both the saddle strategy and the optimal state process exhibit the exponential turnpike property. Namely, for the majority of the time horizon, the distributions of the saddle strategy and the optimal state process closely stay near certain (time-invariant) distributions $ν_1^*$, $ν_2^*$ and $μ^*$, respectively. Additionally, as a byproduct, we solve the infinite horizon version of the differential game and derive closed-loop representations for its open-loop saddle strategy, which has not been proved in the literature. |
| title | Long-Time Behavior of Zero-Sum Linear-Quadratic Stochastic Differential Games |
| topic | Optimization and Control 91A05, 91A15, 49N10, 49N70 |
| url | https://arxiv.org/abs/2406.02089 |