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

目的：该计划的目标是为多智能体网络开发新的博弈论模型和工具，重点是动力学和控制方面。主要研究方向是：（1）基于博弈空间的新分解（潜在的、调和的和非策略的成分）的结构方法;（2）新的解概念（可交换均衡），介于纳什均衡和相关均衡之间。这两种技术都可以有效地应用于实际感兴趣的游戏，因为它们具有方便的计算复杂性。 在应用方面，这些技术将被应用到通信和社交网络的背景下，实际相关的模型，重点是新的分布式动态设计所需的收敛性能。该计划将使新的网络协议和架构，以及改进的实际操作与性能guarantee.The智力优点：重点是应用和扩展有前途的早期结果的结构，表征和解决方案的概念，多人游戏，以及开发新的框架对动态网络的理解和系统的分析。这需要结合博弈论、网络优化、系统论和控制论的思想和数学工具。更广泛的影响：这些方法和技术将有助于动态网络的有效和可靠的设计和操作。这是一个具有明显技术利益、广泛社会影响和明显经济影响的领域。该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，以及与工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.