{"ID":2894521,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.11632","arxiv_id":"2507.11632","title":"Turnpike properties in linear quadratic Gaussian N-player differential games","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2507.11632","url_pdf":"https://arxiv.org/pdf/2507.11632v2","authors":"[\"Asaf Cohen\",\"Jiamin Jian\"]","published":"2025-07-15T18:12:08Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.PR\"]","methods":"[]","has_code":false}