Learning and Control in Multi-Agent Games on Networks

博弈论最近已成为一种不可或缺的工具，可以对传统以及新兴的复杂网络进行分析、建模和设计。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。过去十年见证了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。尽管已经取得了实质性进展，但将传统博弈论应用于复杂现代网络的理解和设计仍面临重大挑战。例如，代理的目标（和决策）会发生干扰，这意味着需要进行协调。然而，集中协调在大型网络（例如自组网络或点对点网络）中通常是不切实际的；或者它消耗过多的带宽和能量。拟议的研究计划重点是将纳什博弈论扩展到多智能体网络。我们的目标是设计最近邻交互规则，实现理想的集体配置（例如纳什均衡），依赖本地可用信息，最大限度地减少多余的通信和处理开销，并在一般类别的游戏和一般对称/非对称网络中证明收敛。我们将重点关注以下主题：（i）了解其他代理，（ii）了解游戏（强化学习），（iii）实现代理的鲁棒性、弹性和处理恶意行为，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，有助于网络游戏的通用统一理论。通过将系统论方法与算子理论、图论和网络相结合，我们将产生新颖的方法和算法，推进网络博弈论的最先进水平。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。这对于我们周围复杂且高度异构的网络非常重要。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以及自主代理网络的设计。它还将带来新网络协议设计以及理解社交网络等网络方面的见解和创新技术。培养博士生5名，硕士生5名，博士后1名。

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.