Multipopulation Aggregative Games: Equilibrium Seeking via Mean-Field Control and Consensus

• 成果类型: Article
• 署名作者: Kebriaei, Hamed; Sadati-Savadkoohi, S. Jafar; Shokri, Mohammad; Grammatico, Sergio
• 署名单位: University of Tehran; Institute for Research in Fundamental Sciences IPM; Delft University of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3057063
• 发表日期: 2021
• 页码: 6011-6016
• 关键词: Aggregative games; consensus; mean-filed; multipopulation; Network games

摘要

In this article, we extend the theory of deterministic mean-field/aggregative games to multipopulation games. We consider a set of populations, each managed by a population coordinator (PC), of selfish agents playing a global noncooperative game, whose cost functions are affected by an aggregate term across all agents from all populations. In particular, we impose that the agents cannot exchange information between themselves directly; instead, only a PC can gather information on its own population and exchange local aggregate information with the neighboring PCs. To seek an equilibrium of the resulting (partial-information) game, we propose an iterative algorithm where each PC broadcasts a mean-field signal, namely, an estimate of the overall aggregative term, to its own population only. In turn, we let the local agents react with the best response and the PCs cooperate for estimating the aggregative term. Our main technical contributions are to cast the proposed scheme as a fixed-point iteration with errors, namely, the interconnection of a Krasnoselskij-Mann iteration and a linear consensus protocol, and, under a nonexpansiveness condition, to show convergence towards an epsilon-Nash equilibrium, where epsilon is inversely proportional to the population size.