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意识的用户自愿为集体利益行事是至关重要的。这种网络的例子出现在智能交通系统、电子商务、智能能源电网和能源市场，以及无线系统中的频谱分配。随着电子连接和计算的使用不断扩大，这些系统正在发生戏剧性的变化，因此可以应用越来越复杂的方法来设计这些网络。该方案旨在将这些网络系统作为具有多个相互作用的战略主体的随机动态系统来研究，其中存在关于系统和彼此的部分信息。特别是，目标是开发一个控制理论框架，以促进此类系统分析的最新水平，并设计新的激励机制，推动代理人的行动实现理想的社会目标。这项研究将与一个重要的教育和推广计划紧密结合在一起，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族裔，进行跨学科研究；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。分析的主旨包括研究一个控制理论框架，通过将代理的均衡策略和信念建模为具有不对称和不完全信息的动态博弈，使系统评估代理的均衡策略和信念成为可能。具体地说，我们计划开发一种系统的方法，为一大类具有不对称信息的动态博弈找到完美的贝叶斯均衡。关联分析建立在博弈论、分散随机控制、马尔可夫决策过程和最优化的基础上。我们设想了一个理论框架，它支持评估均衡的分析工具，就像马尔可夫决策过程的成熟的向后动态规划工具一样。设计的主旨包括调查诱使代理人具有与社会最优目标一致的均衡行为的激励措施，以及开发新的动态机制设计方法。在这里，我们将在动态游戏工作的基础上，探索在分析推力中开发的系统方法论在动态机制设计中的应用。具体地说，我们将研究适合于现实模型的间接动态机制，其中代理具有大的私有类型集但小的操作集。此外，我们将研究拉格朗日松弛方法，它允许更容易和更一般的分析具有时间平均约束的动态机制设计。

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.