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PreprintCC BY 4.0arXiv

Epidemic Control using Stackelberg Mean Field Game with Budget Constraint

  • Huaning Liu
  • Gokce Dayanikli
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Abstract

Epidemic mitigation comes with a price in practice, and when budget is limited, its effective allocation becomes an important question on public policy. In this paper, we study epidemic control through a Stackelberg mean-field game in which a principal, representing the government, chooses social distancing guidelines and vaccination levels for a large population of rational minor agents subject to a budget-spending process. The principal anticipates the minor agents mean-field Nash equilibrium (MFNE) and selects intervention policies to minimize her own objective, inducing a bi-level optimal control problem. We define the Stackelberg mean-field game equilibrium (SMFE) and give its necessary condition by a forward-backward ordinary differential equation (FBODE) system, and provide existence and uniqueness results. We further propose an iterative fixed-point algorithm to solve the FBODE numerically and present computational observations that illustrate the resulting equilibrium behavior.

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Cite

BibTeXRIS
BibTeX
@misc{liu2026epidemic,
  title = {{Epidemic Control using Stackelberg Mean Field Game with Budget Constraint}},
  author = {Huaning Liu and Gokce Dayanikli},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19641},
  eprint = {2609.19641},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19641},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Epidemic Control using Stackelberg Mean Field Game with Budget Constraint
AU  - Huaning Liu
AU  - Gokce Dayanikli
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.19641
UR  - https://arxiv.org/abs/2609.19641
AB  - Epidemic mitigation comes with a price in practice, and when budget is limited, its effective allocation becomes an important question on public policy. In this paper, we study epidemic control through a Stackelberg mean-field game in which a principal, representing the government, chooses social distancing guidelines and vaccination levels for a large population of rational minor agents subject to a budget-spending process. The principal anticipates the minor agents mean-field Nash equilibrium (MFNE) and selects intervention policies to minimize her own objective, inducing a bi-level optimal control problem. We define the Stackelberg mean-field game equilibrium (SMFE) and give its necessary condition by a forward-backward ordinary differential equation (FBODE) system, and provide existence and uniqueness results. We further propose an iterative fixed-point algorithm to solve the FBODE numerically and present computational observations that illustrate the resulting equilibrium behavior.
ER  -