发表机构
Beihang University; School of Mathematical Sciences, Beihang University; Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beihang University; LMIB, Beihang University; Hangzhou International Innovation Institute of Beihang University（北京航空航天大学; 北京航空航天大学数学科学学院; 北京航空航天大学教育部数学、信息学与行为语义重点实验室; 北京航空航天大学数学系; 北京航空航天大学杭州创新研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究两群体线性二次平均场博弈中的异步重规划，识别所需信息为状态-计划对，提出局部算法并分析其稳定性与误差界。
AI 中文摘要
我们研究了两群体线性二次平均场博弈中的异步重规划问题，其中各群体可能从不同的信念出发，因此采用不同的计划。每个群体观察自身的总体轨迹以及已实施修订的公开记录，而其延续最优反应依赖于对手的当前计划。我们确定重规划所需的信息为初始观测区间结束时的总体状态以及对手的活跃延续计划。对于线性观测，该状态-计划对的可恢复性由核包含关系刻画，且有界分解量化了对观测误差的敏感性。特别地，即使完整隐藏信念不可恢复，所需的状态-计划对也可能可恢复。一旦初始化，公开事件记录和共同最优反应映射递归地确定后续对手计划，由此产生的局部算法在每一个有限机会前缀上重现理想基准；由于最优反应的持续性，实施的修订交替进行。对于有限群体，我们推导了采样误差的事件级线性递推，获得有限前缀误差界，并在正决策裕度下证明了自主死区规则的记录匹配性。最后，我们将相互延续响应的唯一可解性与交替响应的稳定性区分开来，并表明在终前Zeno累积点，谱稳定性结合移动边界估计可确保延续计划收敛到从实际极限状态重新启动的均衡。
英文摘要
We study asynchronous continuation replanning in a two-population linear--quadratic mean field game with deterministic open-loop controls and heterogeneous, possibly erroneous initial information. At exogenous opportunities, one population recomputes its continuation response from the physical aggregate state reached, with the opponent's active plan frozen. The state--plan target needed to initialize replanning is recoverable from local aggregate observations if and only if a kernel-inclusion condition holds; full recovery of the hidden initial input is unnecessary. For revisions accumulating before the terminal time, spectral stability of the limiting two-response cycle yields bounded physical execution and a finite state left limit. The zero-extended continuation plans then converge strongly to the mean field equilibrium restarted from that state. A scalar counterexample shows that well-posed continuation problems and a convergent physical state can coexist with divergent remaining plans. We also construct an exact causal implementation from local aggregate observations and establish finite-population robustness on every fixed finite opportunity prefix. Revision records match with probability tending to one, and the mean-square implementation error truncated to the matching event is \(O(N_*^{-1})\), where \(N_*\) is the smaller population size.
