Learning and Control in Multi-Agent Games on Networks

博弈论最近已成为分析、建模和设计传统和新兴复杂网络不可或缺的工具。它是一个强大的数学框架，用于分析合作或竞争决策者(称为参与者或代理人)的战略互动，同时考虑他们的偏好和要求。在过去的十年里，人们对博弈论和网络交叉问题的兴趣激增。在通信网络、智能电网、物联网、社交网络、网络安全、移动服务市场甚至疫情控制等领域，都有许多基于网络的应用。虽然已经取得了实质性的进展，但在将传统博弈论应用于理解和设计复杂的现代网络方面仍存在重大挑战。例如，代理人的目标(和决策)相互干扰，这意味着需要协调。然而，集中式协调在大型网络(例如，临时或对等网络)中通常是不切实际的；或者它消耗过多的带宽和能量。所提出的研究计划侧重于将纳什的博弈论扩展到多代理网络。我们的目标是设计最近邻交互规则，实现理想的集体配置(例如Nash均衡)，依赖本地可用信息，最小化多余的通信和处理开销，并在一般类型的游戏和一般对称/非对称网络上证明是收敛的。我们将重点关注以下主题：(I)学习其他代理，(Ii)学习游戏(强化学习)，(Iii)实现健壮性、弹性和处理代理的恶意行为，以及(Iv)混合学习。从长远来看，我们的计划将产生一个理论框架，为网络游戏的一般统一理论做出贡献。通过将系统论方法与算子理论、图论和网络相结合，我们将产生新的方法和算法，推动网络博弈论的最新发展。这项研究的一些副产品将是在优化网络性能时处理不对称和延迟网络信息的一般规则。这在我们周围复杂且高度异质的网络中非常重要。应用范围从无线网络和社交网络，到智能电网中的需求响应管理和自主代理网络的设计。它还将在设计新的网络协议和理解社交网络等网络方面带来洞察力和创新技术。将培养5名博士生、5名硕士研究生和1名博士后研究员。

Game theory has recently become an indispensable tool enabling the analysis, modeling and design of traditional as well as emerging complex networks. It is a powerful mathematical framework used to analyze strategic interactions of cooperative or competing decision-makers (called players or agents), while taking into account their preferences and requirements. The past decade has witnessed an explosion of interest in issues that intersect game theory and networks. There are many network-based applications in the fields of communication networks, the smart electric grid, the Internet of Things, social networks, network security, mobile service markets or even epidemic control. While there has been substantial progress, there are major challenges in applying traditional game theory to the understanding and design of complex modern networks. For example, the agents' goals (and decisions) interfere and this means that there is need for coordination. However, centralized coordination is often impractical in large networks (e.g. ad-hoc or peer-to-peer networks); or it consumes excessive bandwidth and energy. The proposed research program focuses on the extension of Nash's game theory to multi-agent networks. Our goal is to design nearest-neighbor interaction rules that achieve a desirable collective configuration (e.g. Nash equilibrium), rely on locally available information, minimize superfluous communication and processing overhead, and are provably convergent in general classes of games, and on general symmetric/asymmetric networks. We will focus on the following themes: (i) learning about the other agents, (ii) learning about the game (reinforcement learning), (iii) achieving robustness, resilience and dealing with malicious behaviour of the agents, and (iv) hybrid learning. Long-term our program will generate a theoretical framework that contributes to a general unified theory of games on networks. By combining a system-theoretic approach with operator theory, graph theory and networks, we will generate novel methodologies and algorithms, advancing the state-of-the-art in game theory on networks. Some of the by-products of this research will be general rules to deal with asymmetric and delayed networked information in optimizing network performance. This is important in the complex and highly heterogeneous networks around us. Applications range from wireless networks and social networks, to demand-response management in smart-grids and the design of networks of autonomous agents. It will also lead to insights and innovative technologies in the design of new network protocols, and in understanding networks such as social networks. Five PhD students, five Master students and one post-doctoral fellow will be trained.