  In many stochastic games stemming from financial models, the environment
evolves with latent factors and there may be common noise across agents'
states. Two classic examples are: (i) multi-agent trading on electronic
exchanges, and (ii) systemic risk induced through inter-bank lending/borrowing.
Moreover, agents' actions often affect the environment, and some agent's may be
small while others large. Hence sub-population of agents may act as minor
agents, while another class may act as major agents. To capture the essence of
such problems, here, we introduce a general class of non-cooperative
heterogeneous stochastic games with one major agent and a large population of
minor agents where agents interact with an observed common process impacted by
the mean field. A latent Markov chain and a latent Wiener process (common
noise) modulate the common process, and agents cannot observe them. We use
filtering techniques coupled with a convex analysis approach to (i) solve the
mean field game limit of the problem, (ii) demonstrate that the best response
strategies generate an $\epsilon$-Nash equilibrium for finite populations, and
(iii) obtain explicit characterisations of the best response strategies.
