Risk-sensitive mean field games with major and minor players

We investigate a class of mean field games containing large number major and minor players. Each player minimizes quadratic-tracking type risk-sensitive cost functional, where the reference signal is function state average term To reduce complexity for solving problem, we design sequence decentralized strategies by Nash certainty equivalence principle. Firstly, optimal control problems with quadratic functionals, propose new verification theorem. Secondly, apply two-layer aggregation method to construct fixed-point equations estimations terms give conditions existence uniqueness fixed points. Then, based on local information. It shown that are consistent true values closed-loop systems, designed asymptotic equilibrium. Finally, effectiveness theoretical analysis demonstrated numerical example.