Belief Estimation by Agents in Major-Minor LQG Mean Field Games

Abstract: Motivated by optimal execution in electronic markets where complete market information is not available to traders, we present partially observed LQG mean field games (MFG) consisting of one major agent and a large population of minor agents. We consider the case where the major agent has partial observations of its own state, and each minor agent has partial observations of its own state and the major agent's state. The assumption of partial observations by all agents leads to a new situation involving second-order beliefs (estimates of estimates). This is one of the rare examples of a partially observed game which has a terminating belief of belief recursion. Time permitting, we present an ϵ -Nash equilibrium result for completely observed LQG MFGs with two major agents, and discuss the partial information patterns yielding tractable solutions.

This is joint work with Peter E. Caines.

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