A Survey of Distributed Algorithms for Aggregative Games

Game theory-based models and design tools have gained substantial prominence for controlling and optimizing behavior within distributed engineering systems due to the inherent distribution of decisions among individuals. In non-cooperative settings, aggregative games serve as a mathematical framework model for the interdependent optimal decision-making problem among a group of non-cooperative players. In such scenarios, each player's decision is influenced by an aggregation of all players' decisions. Nash equilibrium (NE) seeking in aggregative games has emerged as a vibrant topic driven by applications that harness the aggregation property. This paper presents a comprehensive overview of the current research on aggregative games with a focus on communication topology. A systematic classification is conducted on distributed algorithm research based on communication topologies such as undirected networks, directed networks, and time-varying networks. Furthermore, it sorts out the challenges and compares the algorithms' convergence performance. It also delves into real-world applications of distributed optimization techniques grounded in aggregative games. Finally, it proposes several challenges that can guide future research directions.