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Center for Nonlinear Studies |
There exist many real world situations involving multiple decision makers, cooperative or strategic, in a stochastic dynamical system with decentralized information. Such scenarios include communication systems, social networks, energy markets and many others. In this talk, we present structural results and analytical tools to study a class of such systems. (i) We first study energy-delay trade-off in a relay channel, as a prototype example of decentralized team problems (with cooperative users). The model extends to many other scenarios like sensor and surveillance networks, spatially distributed systems like power generation and transmission systems etc. Using two key ideas from the literature, we present a dynamic programming formulation to find optimum policies. (ii) Extending the previous model for strategic users, we study a general class of dynamic games with asymmetric information and independent types. An appropriate notion of equilibria for such games is perfect Bayesian equilibria (PBE). There does not exist any methodology for finding PBE for general dynamic games. For the games considered, we present a sequential decomposition algorithm, similar in flavor to dynamic programming, to find a class of PBEs. Based on this methodology, we prese nt a general framework to study Bayesian learning dynamics in social networks. In a series of seminal papers in the literature, a simplifying model was studied with myopic, selfish agents, demonstrating herding behavior among agents, also termed as informational cascades. We present a more general model where players participate throughout the process, and for a specific learning model considered, we characterize its informational cascades, where learning stops for the team as a whole. Deepanshu Vasal is a final year PhD student in Electrical Engineering: Systems at University of Michigan, Ann Arbor. He received M.S. degrees in Electrical Engineering and Computer Science (EECS), and in Mathematics from University of Michigan, Ann Arbor, in 2011 and 2013, respectively. Prior to that, he received the BTech degree in Electronics and Communication Engineering from the Indian Institute of Technology, Guwahati, India, in 2009. Deepanshu's fields of interest include Applied Probability, Decentralized control, Social networks and learning, and Information Theory. He is a recipient of EECS department fellowship at University of Michigan, Ann Arbor, in Winter 2015.