发表机构
The Hong Kong University of Science and Technology（香港科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对R^d上的图on平均场系统，建立欧拉逼近、证明边缘凸序保持性，结合加权L^2范数得到无限时间水平轨迹收敛结果，并将其应用于图on平均场博弈的值函数比较。
AI 中文摘要
本文研究R^d上图on平均场系统的凸序保持性。首先，我们建立所关注的图on平均场系统的时间一致欧拉逼近，这推广了Bayraktar和Wu（SPA，2022）关于图on粒子系统的已有结果，且对我们的主要定理是必要的。结合图on函数的适当条件，我们随后证明边缘凸序保持性。其次，通过使用加权L^2范数，我们进一步建立无限时间水平轨迹层面的收敛结果，这是Liu和Pages（AAP，2023）所研究的泛函凸序的关键。最后，我们将结果应用于图on平均场博弈（MFGs）的值函数比较研究。
英文摘要
We establish marginal and functional convex order comparisons for graphon mean-field systems on $\mathbb{R}^d$, 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 $[0,\infty)$. As an application, we derive value-function comparisons for a class of one-dimensional linear-quadratic graphon mean-field games.
