闭环与开环线性二次N人微分博弈的定量比较
Quantitative comparison of closed- and open-loop linear-quadratic $N$-player differential games
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中文总结 AI 辅助
本文定量比较有限时域随机线性二次N人博弈中的闭环与开环纳什均衡，通过引入参考博弈和扰动博弈，证明在弱扰动下两者渐近等价，无需平均场极限。
中文摘要 AI 辅助
我们在一个具有解耦状态动力学和通过状态成本相互作用的有限时域随机线性二次N人博弈中，比较了闭环和开环纳什均衡。我们引入了一个块对角参考博弈和一个邻近的扰动博弈，并在两种信息结构下分别研究它们。闭环和开环问题导致不同的Riccati系统，但对于参考博弈，它们诱导的均衡状态和控制过程完全一致。然后，我们证明了在状态成本的弱扰动下的可解性和稳定性，从而得到相应均衡之间的定量界。特别地，当扰动随人口规模足够快地减小时，扰动博弈的闭环和开环均衡变得渐近等价。该比较直接在有限玩家层面进行，无需可交换性或平均场极限。
英文摘要
We compare closed-loop and open-loop Nash equilibria in a finite-horizon stochastic linear-quadratic $N$-player game with decoupled state dynamics and interaction through the state costs. We introduce a block-diagonal reference game and a nearby perturbed game, and study each under both information structures. The closed-loop and open-loop problems lead to different Riccati systems, but for the reference game their induced equilibrium state and control processes coincide exactly. We then prove solvability and stability under weak perturbations of the state costs, yielding quantitative bounds between the corresponding equilibria. In particular, when the perturbation decreases sufficiently fast with the population size, the closed-loop and open-loop equilibria of the perturbed game become asymptotically equivalent. The comparison is carried out directly at the finite-player level, without requiring exchangeability or a mean-field limit.
发表机构
- University of Michigan（密歇根大学）
机构由 AI 辅助整理，请以论文原文为准。
