Discrete-Time Mean Field Partially Observable Controlled Systems Subject to Common Noise

Abstract

In this article, we provide the first systemic study on discrete time partially observable mean field systems in the presence of a common noise. Each player makes decision solely based on the observable process. Both the mean field games and the related tractable mean field type stochastic control problem are studied. We first solve the mean field type control problem using classical discrete time Kalman filter with notable modifications. The unique existence of the resulted forward backward stochastic difference system is then established by separation principle. The mean field game problem is also solved via an application of stochastic maximum principle, while the existence of the mean field equilibrium is shown by the Schauder’s fixed point theorem.