Asynchronous Replanning in Two Population Linear Quadratic Mean Field Games: Information Requirements and Stability
Abstract
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.
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BibTeX
@misc{jin2026asynchronous,
title = {{Asynchronous Replanning in Two Population Linear Quadratic Mean Field Games: Information Requirements and Stability}},
author = {Yuxin Jin and Wang Yao and Xiao Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.11424},
eprint = {2609.11424},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11424},
}
RIS
TY - UNPB
TI - Asynchronous Replanning in Two Population Linear Quadratic Mean Field Games: Information Requirements and Stability
AU - Yuxin Jin
AU - Wang Yao
AU - Xiao Zhang
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2609.11424
UR - https://arxiv.org/abs/2609.11424
AB - 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.
ER -