一般领导者-跟随者线性二次随机图博弈（含不定控制权重）
General Leader-Follower Linear-Quadratic Stochastic Graphon Games with Indefinite Control Weights
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中文总结 AI 辅助
研究含不定控制权重的领导者-跟随者线性二次随机图博弈，通过随机最大值原理刻画均衡，构造Stackelberg-纳什均衡并设计分散策略，推广了现有模型。
中文摘要 AI 辅助
本文研究具有不定控制权重的一般领导者-跟随者线性二次随机图博弈。该模型由一个领导者和连续统的跟随者组成，其中跟随者通过图聚合项相互作用，并通过其动力学和成本泛函与领导者耦合。与现有相关模型相比，本文考虑的状态方程允许更一般的扩散项，包括依赖于状态、控制、领导者变量和图聚合项的扩散系数。利用随机最大值原理，我们通过带有图聚合项的耦合正倒向随机系统刻画了跟随者的纳什响应和领导者的最优控制。在适当的Riccati可解性和凸性条件下，我们为极限图博弈构造了一个Stackelberg-纳什均衡。我们进一步为相关的有限玩家网络博弈设计了分散策略，并证明它们构成近似Stackelberg-纳什均衡，从而得到混沌传播结果。该框架作为特例涵盖了不定线性二次随机图博弈、Stackelberg平均场博弈以及具有随机效应的随机图博弈。
英文摘要
This paper studies general leader-follower linear-quadratic stochastic graphon games with indefinite control weights. The model consists of one leader and a continuum of followers, where the followers interact through graphon aggregate terms and are coupled with the leader through their dynamics and cost functionals. Compared with existing related models, the state equations considered here allow more general diffusion terms, including diffusion coefficients depending on the states, controls, leader variables, and graphon aggregate terms. Using the stochastic maximum principle, we characterize the followers' Nash response and the leader's optimal control through coupled forward-backward stochastic systems with graphon aggregate terms. Under suitable Riccati solvability and convexity conditions, we construct a Stackelberg-Nash equilibrium for the limiting graphon game. We further design decentralized strategies for the associated finite-player network game and prove that they form an approximate Stackelberg-Nash equilibrium, which yields a propagation of chaos result. The framework covers, as special cases, indefinite linear-quadratic stochastic graphon games, Stackelberg mean field games, and stochastic graphon games with random effects.
发表机构
- School of Mathematics, Shandong University（山东大学数学学院）
机构由 AI 辅助整理，请以论文原文为准。
