ε-Nash equilibria for partially observed LQG mean field games with major agent: Partial observations by all agents

LQG mean field systems with a major agent (i.e. non-asymptotically vanishing as the population size goes to infinity) and a population of minor agents (i.e. individually asymptotically negligible) are studied in (Huang, 2010) and (Nguyen and Huang, 2012). Due to presence of the major agent, the mean field becomes stochastic in contrast to the case with purely minor agents where mean field is deterministic (Huang et al 2007). In (Caines and Kizilkale, 2013, 2014, ŗen and Caines 2013, 2014), it is assumed the major agent´s state is partially observed by each minor agent, and the major agent completely observes its own state. Accordingly, each minor agent can recursively estimate the major agent´s state, compute the system´s mean field and thence generate the feedback control which yields ε-Nash equilibrium property. This paper investigates the problem of estimation and control for an LQG mean field system in which both the major agent and the minor agents partially observe the major agent´s state. The existence of ε-Nash equilibria together with the individual agents´ control laws yielding the equilibria are established wherein each agent recursively generates estimates of the major agent´s state and hence generates a version of the system´s mean field.