  In this paper, we consider a discrete-time Stackelberg mean field game with a
leader and an infinite number of followers. The leader and the followers each
observe types privately that evolve as conditionally independent controlled
Markov processes. The leader commits to a dynamic policy and the followers best
respond to that policy and each other. Knowing that the followers would play a
mean field game based on her policy, the leader chooses a policy that maximizes
her reward. We refer to the resulting outcome as a Stackelberg mean field
equilibrium (SMFE). In this paper, we provide a master equation of this game
that allows one to compute all SMFE. Based on our framework, we consider two
numerical examples. First, we consider an epidemic model where the followers
get infected based on the mean field population. The leader chooses subsidies
for a vaccine to maximize social welfare and minimize vaccination costs. In the
second example, we consider a technology adoption game where the followers
decide to adopt a technology or a product and the leader decides the cost of
one product that maximizes his returns, which are proportional to the people
adopting that technology
