A control-theoretic framework for analysis and design of networked systems with strategic agents via structured strategies

为了现代社会网络的正常运作，激励参与这些网络的具有战略头脑的用户自愿为集体利益而行动是至关重要的。这种网络的例子出现在智能交通系统、电子商务、智能电网和能源市场，以及无线系统中的频谱分配。由于电子连接和计算的不断扩展，这些系统正在发生巨大的变化，因此越来越复杂的方法可以应用于这些网络的工程设计。本研究的目的是将这些网络系统作为随机动力系统来研究，这些系统具有策略代理，在存在系统和彼此的部分信息的情况下具有多种交互作用。特别是，目标是发展一个控制理论框架，以推进对此类系统的分析的艺术状态，并设计新的激励方案，推动代理人的行动朝着理想的社会目标发展。这项研究将与一项重要的教育和推广计划紧密结合，该计划包括两个重点领域：培训学生，包括本科生和代表性不足的少数民族，进行跨学科研究；并以新课程开发和学生参与的形式广泛传播研究成果。该提案将追求两个协同推进，一个侧重于分析，另一个侧重于设计。分析重点包括研究一个控制理论框架，通过将代理人的相互作用建模为具有不对称和不完全信息的动态博弈，该框架将能够系统地评估代理人的均衡策略和信念。具体来说，我们计划开发一种系统的方法，用于寻找具有不对称信息的大类动态博弈的完美贝叶斯均衡。相关的分析建立在博弈论，分散随机控制，马尔可夫决策过程和优化的基础上。我们设想了一个理论框架，该框架支持均衡评估的分析工具，就像马尔可夫决策过程的成熟的向后动态规划工具一样。设计主旨包括研究诱导主体产生符合社会最优目标的均衡行为的激励机制，以及发展新的动态机制设计方法。在这里，我们将通过探索在动态机制设计分析中开发的系统方法的应用来构建动态博弈的工作。具体来说，我们将研究适用于具有大型私有类型集但小型动作集的代理的现实模型的间接动态机制。此外，我们将研究拉格朗日松弛方法，该方法允许对具有时间平均约束的动态机构设计进行更容易和更一般的分析。

For the proper functioning of modern societal networks it is critical to incentivize strategically minded users participating in these networks to voluntarily act in the interest of the collective. Examples of such networks arise in intelligent transportation systems, electronic commerce, smart energy grid and energy markets, and spectrum allocation in wireless systems. These systems are being dramatically transformed by the ever-expanding use of electronic connectivity and computation so that increasingly sophisticated approaches can be applied for engineering these networks. This proposal aims to study these networked systems as stochastic dynamical systems with strategic agents having multiple interactions in the presence of partial information about the system and each other. In particular, the goal is to develop a control-theoretic framework to advance the state of the art for the analysis of such systems, and also to design novel incentive schemes that drive the agents' actions towards desirable social objectives. The research will be tightly integrated with a significant education and outreach program consisting of two focus areas: training students, including undergraduates and underrepresented minorities, in interdisciplinary research; and broadly disseminating research outcomes in the form of new curricular development and student involvement. The proposal will pursue two synergistic thrusts, one focusing on analysis and the other on design. The analysis thrust consists of investigating a control-theoretic framework that will enable the systematic evaluation of the agents' equilibrium strategies and beliefs, by modeling their interactions as a dynamic game with asymmetric and imperfect information. Specifically, we plan to develop a systematic methodology for finding Perfect Bayesian Equilibria for a broad class of dynamic games with asymmetric information. The associated analysis builds upon foundations in game theory, decentralized stochastic control, Markov decision processes and optimization. We envision a theoretical framework that supports analytical tools for the evaluation of equilibria much like the well-established backward dynamic programming tools for Markov decision processes. The design thrust consists of investigating incentives that induce agents to have an equilibrium behavior consistent with a socially optimal objective, and developing new dynamic mechanism design methodologies. Here, we will build upon the work on dynamic games by exploring applications of the systematic methodology developed in the analysis thrust to dynamic mechanism design. Specifically, we will investigate indirect dynamic mechanisms that are appropriate for realistic models with agents having large private type-sets but small action sets. Furthermore, we will investigate Lagrangian relaxation methods that allow for an easier and more general analysis of dynamic mechanism design with time-average constraints.