Speaker: Nevroz Sen
Title: Partially Observed Mean Field Game Theory
Abstract: Subject to reasonable conditions, in large population stochastic dynamic games where the agents are coupled in a mean field manner through their dynamics and their cost functions, Mean Field Game (MFG) theory demonstrates that a best response control action for each agent exists which depends only upon the individual agent’s state observations and the deterministic distribution of population states (the system mean field). Furthermore, such decentralized control actions achieve an ε-Nash equilibrium for the system. Within this framework, one can incorporate the so-called major agent into the game which has asymptotically non-negligible influence on each other agent (referred to as minor agents). The consequences of the existence of a major agent are two folds; (i) the mean field becomes stochastic due to the stochastic evolution of the state of the major agent and (ii) the best response control actions of the other agents depend on the state of the major agent as well as the stochastic mean field. In a decentralized environment, one is led to consider the situation where minor agents are provided only with partial information on the major agent’s state. In the first part of this talk such a scenario is considered for systems with nonlinear dynamics and nonlinear cost functions and an ε-Nash MFG theory is developed. We next discuss the situation where each agent has only partial observations on its individual state. The approach for both problems is to follow the procedure of constructing the associated completely observed system via the application of nonlinear filtering theory and the Separation Principle in the infinite population game. Work with Peter E. Caines.
Bio: Nevroz Sen received his Ph.D. degree from Queen’s University, Kingston, ON, Canada, in mathematics and engineering in 2013. He worked as a postdoctoral fellow at the Department of Electrical and Computer Engineering at McGill University, Montreal, QC, Canada, and at the School of Engineering and Applied Sciences at Harvard University, Cambridge, MA, in 2013-16 and 2016-17, respectively. His research interests include mean field game theory, nonlinear filtering, information theory and stochastic control.