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

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  • Deepanshu Vasal
  • Randall Berry

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

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  • Deepanshu Vasal & Randall Berry, 2022. "Master Equation for Discrete-Time Stackelberg Mean Field Games with single leader," Papers 2201.05959, arXiv.org.
    • Handle: RePEc:arx:papers:2201.05959
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    File URL: http://arxiv.org/pdf/2201.05959
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    Cited by:

    1. Deepanshu Vasal, 2022. "Master equation of discrete-time Stackelberg mean field games with multiple leaders," Papers 2209.03186, arXiv.org.
    2. Sina Sanjari & Subhonmesh Bose & Tamer Başar, 2025. "Incentive Designs for Stackelberg Games with a Large Number of Followers and their Mean-Field Limits," Dynamic Games and Applications, Springer, vol. 15(1), pages 238-278, March.

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