We investigate the problem of estimation and control for LQG mean field game systems in which both the major agent and the minor agents partially observe the major agent's state. The existence of epsilon-Nash equilibria together with the individual agents' control laws yielding the equilibria is established wherein each agent recursively generates estimates of the major agent's state and hence generates a version of the system's mean field.
An initial formulation of an application of this work to linearized versions of the optimal execution problem in the financial sector is then presented where an institutional investor, interpreted as a major agent, has partial observations of its own inventories, and high frequency traders (HFTs), interpreted as minor agents, have partial observations of the major agent's inventories. The objective of each agent is to maximize its own wealth.
This is joint work with Peter E. Caines.