Novel Game-Theoretic Tools and Solution Concepts with Applications to Network Dynamics and Control

目的：本项目的目标是为多智能体网络开发新的博弈论模型和工具，重点放在动力学和控制方面。主要的研究方向是：(I)基于博弈空间(势、调和和非战略分量)的新颖分解的结构化方法；(Ii)新的解概念(可交换均衡)，介于Nash和相关均衡之间。这两种技术都可以有效地应用于有实际意义的游戏，因为它们具有方便的计算复杂性特性。在应用方面，这些技术将应用于通信和社会网络背景下的实际相关模型，重点是设计具有理想收敛特性的新的分布式动态。拟议的计划将使新的网络协议和体系结构成为可能，并在性能保证的情况下改进实际操作。智力优势：重点是应用和推广多人游戏的结构、特征和解决方案概念方面的有希望的早期成果，以及为理解和系统分析动态网络开发新的框架。这需要博弈论、网络优化、系统论和控制论的思想和数学工具的结合。广泛的影响：这些方法和技术将有助于动态网络的高效和可靠的设计和运行。这是一个具有明显的技术利益、广泛的社会影响和明显的经济影响的领域。这项提案的其他主要特点包括与课程开发、本科研究项目、计算优化新项目的整合，以及与行业合作伙伴和政府研究实验室的密切合作。

Objective: The objective of this program is to develop new game-theoretic models and tools for multi-agent networks, with emphasis on dynamics and control aspects. The main research thrustsare: (i) structural approaches based on novel decompositions of the space of games (in terms of potential, harmonic, and nonstrategic components); (ii) new solution concepts (exchangeable equilibria), intermediate between Nash and correlated equilibria. Both techniques can be effectively applied to games of practical interest, since they enjoy convenient computational complexity properties. On the application side, the techniques will be applied to practically relevant models in the context of communication and social networks, with emphasis on the design of new distributed dynamics with desirable convergence properties. The proposed program will enable new network protocols and architectures, as well as improved practical operation with performance guarantees.The intellectual merit: The focus is to apply and extend promising early results on structure, characterization, and solution concepts of multiplayer games, as well as to develop new frameworks towards the understanding and systematic analysis of dynamic networks. This requires the combination of ideas and mathematical tools from game theory, network optimization, systems theory, and control theory.Broader impact: The methods and techniques will contribute to the efficient and reliable design and operation of dynamic networks. This is an area of clear technological interest, wide societal impact, and obvious economic implications. Other key features of this proposal include its integration with curriculum development, undergraduate research projects, new programs on computational optimization, and close collaboration with industrial partners and government research labs.