标题： 线性二次高斯N人微分博弈中的Turnpike性质 显示英文标题

标题： Turnpike properties in linear quadratic Gaussian N-player differential games

摘要： 我们考虑在具有高斯初始数据的线性二次$N$-玩家博弈中平衡策略和状态轨迹的长期行为。 通过分析收敛到相应的遍历博弈，我们建立了有限时间范围Riccati系统与遍历设置中出现的相关代数Riccati系统之间的指数收敛估计。 基于这些结果，我们证明了时间平均值函数的收敛性，并为每个玩家的平衡对推导出一个turnpike性质。 重要的是，我们的方法避免依赖于均场博弈极限模型，使得相对于玩家数量$N$的分析完全一致。 因此，我们进一步建立了有限时间范围博弈与遍历博弈之间具有$N$名玩家的平衡对的统一turnpike性质。 显示英文摘要

摘要： We consider the long-time behavior of equilibrium strategies and state trajectories in a linear quadratic $N$-player game with Gaussian initial data. By analyzing convergence toward the corresponding ergodic game, we establish exponential convergence estimates between the solutions of the finite-horizon Riccati system and the associated algebraic Riccati 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.