Master Equation for Discrete-Time Stackelberg Mean Field Games with single leader
Abstract
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
- Publication:
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arXiv e-prints
- Pub Date:
- January 2022
- DOI:
- 10.48550/arXiv.2201.05959
- arXiv:
- arXiv:2201.05959
- Bibcode:
- 2022arXiv220105959V
- Keywords:
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- Electrical Engineering and Systems Science - Systems and Control;
- Computer Science - Computer Science and Game Theory;
- Economics - Theoretical Economics;
- Mathematics - Optimization and Control
- E-Print:
- 25 pages. arXiv admin note: text overlap with arXiv:2005.01997