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.

I. Introduction

The 6th generation (6G) mobile communication networks have been expected to realize wide-area intelligent connection of everything. Meanwhile, driven by business requirements and technical developments, the 6G will also encounter novel challenges of wider network coverage density, high-volume mobile data traffic, and smart resource management and control due to large-scale deployment of network nodes. In industrial products, SpaceX has developed a novel Starlink satellite orbit, and eventually hopes to have as many as 42,000 satellites in this mega-constellation [1]. According to new research, SpaceX filings in the International Telecommunication Union database have found that nations worldwide plan to launch more than 1 million satellites in 300 mega-constellations to enable global satellite Internet services [2]. Furthermore, global Internet growth and trends are anticipated to attain double-digit growth between 2017 and 2022, and the volume of mobile communication data will exceed one zettabyte/mo by 2028 [3], [4]. The realization of coupled working mode coexistence for dense network nodes is the key issue for future 6G networking. In the air, unmanned aerial vehicles (UAVs)-assisted networking emerges as a seminal and indispensable method for solving existing issues [5]. On the one hand, flexible deployment of UAVs can handle many new business applications. On the other hand, it can also improve data processing performance and network capacity. Moreover, cellular communications [6], [7] and device-to-device (D2D) communications [8] to achieve partitioning of the networking space into several small cells, which provides sufficient incentives to realize near-end communication on the ground. It will constitute one promising technology for meeting the surging user demands in the future 6G era, referred to as ultra-dense space-air-ground network.1 This network paradigm integrates space, air, and ground networks to achieve ultra-dense, high dynamic, and heterogeneous characteristics [9], [10], meets wider spatial coverage and faster data transmission rates, and provides real-time, reliable communication connectivity for various application scenarios. The strategic positioning of this technology aims to effectively address the anticipated surge in user demands in the forthcoming 6G era.¹

In this work, “ultra-dense space-air-ground network” and “ultra-dense networks (UDNs)” are assigned the same meaning for the convenience of readers.