ε-Nash equilibria for a partially observed mean field game with major player

Consider a dynamic game with a population of N minor agents, where N is very large, and a major agent where the agents are coupled in their nonlinear dynamics and cost functions such that even asymptotically as the population size goes to infinity the major agent has a non-vanishing effect on the minor agents. Such games are referred to as mean field games with major-minor agents (MM-MFG) and for MM-MFG, it has been demonstrated the mean field term is stochastic and the best response control actions of the minor agents depend on the state of the major agent as well as this stochastic mean field. In practical applications one is led to consider the situation where the minor agents partially observe (PO) the state of the major agent. In this work, we consider a restricted case of this scenario and demonstrate that in the case the minor agents are coupled to the major agent only through their cost functions, one can obtain the ε-Nash equilibrium property for the PO-MM-MFG best response control actions as the population size N goes to infinity.