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In this paper, we consider a discrete-time Stackelberg mean field game with aleader and an infinite number of followers. The leader and the followers eachobserve types privately that evolve as conditionally independent controlledMarkov processes. The leader commits to a dynamic policy and the followers bestrespond to that policy and each other. Knowing that the followers would play amean field game based on her policy, the leader chooses a policy that maximizesher reward. We refer to the resulting outcome as a Stackelberg mean fieldequilibrium (SMFE). In this paper, we provide a master equation of this gamethat allows one to compute all SMFE. Based on our framework, we consider twonumerical examples. First, we consider an epidemic model where the followersget infected based on the mean field population. The leader chooses subsidiesfor a vaccine to maximize social welfare and minimize vaccination costs. In thesecond example, we consider a technology adoption game where the followersdecide to adopt a technology or a product and the leader decides the cost ofone product that maximizes his returns, which are proportional to the peopleadopting that technology

Master Equation for Discrete-Time Stackelberg Mean Field Games with single leader