TY - GEN
T1 - Master Equation for Discrete-Time Stackelberg Mean Field Games with a Single Leader
AU - Vasal, Deepanshu
AU - Berry, Randall
N1 - Publisher Copyright:
© 2022 IEEE.
PY - 2022
Y1 - 2022
N2 - In this paper, we consider a discrete-time Stack-elberg 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.
AB - In this paper, we consider a discrete-time Stack-elberg 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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U2 - 10.1109/CDC51059.2022.9993218
DO - 10.1109/CDC51059.2022.9993218
M3 - Conference contribution
AN - SCOPUS:85147042315
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 5529
EP - 5535
BT - 2022 IEEE 61st Conference on Decision and Control, CDC 2022
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 61st IEEE Conference on Decision and Control, CDC 2022
Y2 - 6 December 2022 through 9 December 2022
ER -