A UNIFIED APPROACH TO LINEAR-QUADRATIC-GAUSSIAN MEAN-FIELD TEAM: HOMOGENEITY, HETEROGENEITY AND QUASI-EXCHANGEABILITY

• 成果类型: Article
• 署名作者: Feng, Xinwei; Hu, Ying; Huang, Jianhui
• 署名单位: Shandong University; Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); Hong Kong Polytechnic University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1878
• 发表日期: 2023
• 页码: 2786-2823
• 关键词: variance portfolio selection; n-player games; Nash equilibria; CONVERGENCE

摘要

This paper aims to systematically solve stochastic team optimization of a large-scale system, in a linear-quadratic-Gaussian framework. Concretely, the underlying large-scale system involves considerable weakly coupled co-operative agents for which the individual admissible controls: (i) enter the diffusion terms, (ii) are constrained in some closed-convex subsets and (iii) subject to a general partial decentralized information structure. A more im-portant but serious feature: (iv) all agents are heterogenous with continuum instead of finite diversity. Combination of (i)-(iv) yields a quite general mod-eling of stochastic team-optimization, but on the other hand, also fails current existing techniques of team analysis. In particular, classical team consistency with continuum heterogeneity collapses because of (i). As the resolution, a novel unified approach is proposed under which the intractable continuum heterogeneity can be converted to a more tractable homogeneity. As a trade-off, the underlying randomness is augmented, and all agents become (quasi) weakly exchangeable. Such an approach essentially involves a subtle bal-ance between homogeneity v.s. heterogeneity, and left (prior -sampling)-v.s. right (posterior-sampling) information filtration. Subsequently, the consis-tency condition (CC) system takes a new type of forward-backward stochastic system with double-projections (due to (ii), (iii)), along with spatial mean on continuum heterogenous index (due to (iv)). Such a system is new in team literature and its well-posedness is also challenging. We address this issue under mild conditions. Related asymptotic optimality is also established.