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

arXiv: https://arxiv.org/abs/2201.05959 · HTML: https://mlsanity.com/paper/2201.05959/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2022.

## Built on by (most cited first, 3 of 3)

- [Model-Based RL for Mean-Field Games is not Statistically Harder than Single-Agent RL](https://mlsanity.com/paper/2402.05724/) (2024)
- [Learning Discrete-Time Major-Minor Mean Field Games](https://mlsanity.com/paper/2312.10787/) (2023)
- [Bounded Rationality Equilibrium Learning in Mean Field Games](https://mlsanity.com/paper/2411.07099/) (2024)

## Abstract (arXiv)

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