Distributed Non-Cooperative Games and Distributed Learning in Linear and Nonlinear Systems: An Overview

As an important research direction of distributed intelligence, distributed non-cooperative game (DNCG) mainly involves algebraic graph theory, distributed learning, multi-agent system (MAS) and distributed control theory, which has been received more and more attention. Although significant progress has been made in solving DNCGs, DNCGs in linear and nonlinear systems based on distributed learning methods have not been fully summarized. Therefore, based on distributed learning methods, this paper provides a recent review of distributed zero-sum games (DZSGs) in linear and nonlinear systems. First, the classical directed communication graphs widely used in DZSGs with a fixed topological structure have been investigated. Second, this paper details the four types of MASs suitable for DZSGs, which are prepared for the introduction of DZSGs below. Then, a table summarizes the 12 types of classical MASs that have been widely used in DZSGs. Moreover, the DZSG problems in four types of linear and nonlinear systems have also been investigated, which established a foundation for the subsequent distributed algorithms. Furthermore, this article simultaneously studied the existing classic distributed algorithms for DZSG problems under four different system types, which presented the research status of DZSG problems for 12 systems in the form of a table. Finally, the further research directions of DNCGs have been summarized and the promising and challenging research directions for the future have also been proposed in the paper.