A Survey on Mean-Field Game for Dynamic Management and Control in Space-Air-Ground Network

The data traffic volume of the 6th generation (6G) mobile communication networks is huge, and there are novel challenges in various communications services and scenarios. This calls for ultra-dense and heterogeneous deployments of network nodes both on the ground and in space, resulting in ultra-dense space-air-ground network. However, conventional models are not available to analyze and design the interactions among heterogeneous network nodes. Game theory can provide an effective mathematical modeling framework for analysis and design. For the 6G space-air-ground networks, the characteristics of stochastic, ultra-dense, and distributed control will cause conventional game theoretical approaches to confront the challenge of the curse of dimensionality. Mean-field game (MFG) can be introduced to decouple dynamic management and control among agents, to decouple their interactions in a high-dimensional regime. Although the MFG finds wide application, there lacks a comprehensive survey to clarify the basics and summarize the state of the art of MFG research status. In this survey, we investigate and provide an overview of the applications of the MFG. First, we discuss diverse 6G space-air-ground networking paradigms, and then introduce the basic concepts of the MFG. Second, various MFG-based optimal control policies together with mean-field equilibrium (MFE) solutions are investigated and surveyed. Moreover, we discuss the effectiveness of combining the MFG with other game-theoretic approaches and machine learning methods, which leads to the improvement of multi-agent system performances. Finally, we outline some open issues, technical challenges, and future research directions based on the current state of the art.