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

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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.