Turnpike properties in linear quadratic Gaussian N-player differential games
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908944698441728 |
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| author | Cohen, Asaf Jian, Jiamin |
| author_facet | Cohen, Asaf Jian, Jiamin |
| contents | We consider the long-time behavior of equilibrium strategies and state trajectories in a linear quadratic $N$-player game with Gaussian initial data. By comparing the finite-horizon game with its ergodic counterpart, we establish exponential convergence estimates between the solutions of the finite-horizon generalized Riccati system and the associated algebraic system arising in the ergodic setting. Building on these results, we prove the convergence of the time-averaged value function and derive a turnpike property for the equilibrium pairs of each player. Importantly, our approach avoids reliance on the mean field game limiting model, allowing for a fully uniform analysis with respect to the number of players $N$. As a result, we further establish a uniform turnpike property for the equilibrium pairs between the finite-horizon and ergodic games with $N$ players. Numerical experiments are also provided to illustrate and support the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11632 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Turnpike properties in linear quadratic Gaussian N-player differential games Cohen, Asaf Jian, Jiamin Optimization and Control Probability 91A15, 49N10, 91A23, 49N70, 34H05 We consider the long-time behavior of equilibrium strategies and state trajectories in a linear quadratic $N$-player game with Gaussian initial data. By comparing the finite-horizon game with its ergodic counterpart, we establish exponential convergence estimates between the solutions of the finite-horizon generalized Riccati system and the associated algebraic system arising in the ergodic setting. Building on these results, we prove the convergence of the time-averaged value function and derive a turnpike property for the equilibrium pairs of each player. Importantly, our approach avoids reliance on the mean field game limiting model, allowing for a fully uniform analysis with respect to the number of players $N$. As a result, we further establish a uniform turnpike property for the equilibrium pairs between the finite-horizon and ergodic games with $N$ players. Numerical experiments are also provided to illustrate and support the theoretical results. |
| title | Turnpike properties in linear quadratic Gaussian N-player differential games |
| topic | Optimization and Control Probability 91A15, 49N10, 91A23, 49N70, 34H05 |
| url | https://arxiv.org/abs/2507.11632 |