Convex ordering for graphon mean-field systems
Abstract
We establish marginal and functional convex order comparisons for graphon mean-field systems on ℝd, including the infinite-horizon setting. A key difficulty is that convex order cannot in general be transferred through the usual particle approximation, which requires us to work directly with Euler schemes for the graphon mean-field system. Under a suitable dissipativity condition, we establish Euler approximation estimates that are uniform in both time and the agent label, and combine them with forward-backward induction arguments to obtain the convex order comparisons. For the infinite-horizon problem, dissipativity provides the required uniform-in-time stability, while an exponentially weighted L2-space enables trajectory-level convergence and leads to the functional convex order on [0,∞). As an application, we derive value-function comparisons for a class of one-dimensional linear-quadratic graphon mean-field games.
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BibTeX
@misc{cui2026convex,
title = {{Convex ordering for graphon mean-field systems}},
author = {Daorong Cui and Shuoqing Deng and Yang Xiang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.19576},
eprint = {2608.19576},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.19576},
}
RIS
TY - UNPB
TI - Convex ordering for graphon mean-field systems
AU - Daorong Cui
AU - Shuoqing Deng
AU - Yang Xiang
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2608.19576
UR - https://arxiv.org/abs/2608.19576
AB - We establish marginal and functional convex order comparisons for graphon mean-field systems on ℝ^d, including the infinite-horizon setting. A key difficulty is that convex order cannot in general be transferred through the usual particle approximation, which requires us to work directly with Euler schemes for the graphon mean-field system. Under a suitable dissipativity condition, we establish Euler approximation estimates that are uniform in both time and the agent label, and combine them with forward-backward induction arguments to obtain the convex order comparisons. For the infinite-horizon problem, dissipativity provides the required uniform-in-time stability, while an exponentially weighted L^2-space enables trajectory-level convergence and leads to the functional convex order on [0,∞). As an application, we derive value-function comparisons for a class of one-dimensional linear-quadratic graphon mean-field games.
ER -