# Optimal incentives to mitigate epidemics: a Stackelberg mean field game approach

arXiv: https://arxiv.org/abs/2011.03105 · HTML: https://mlsanity.com/paper/2011.03105/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Nov 2020.

## Built on by (most cited first, 9 of 9)

- [Learning Correlated Equilibria in Mean-Field Games](https://mlsanity.com/paper/2208.10138/) (2022)
- [Neural Operators Can Play Dynamic Stackelberg Games](https://mlsanity.com/paper/2411.09644/) (2024)
- [Learning Mean Field Games on Sparse Graphs: A Hybrid Graphex Approach](https://mlsanity.com/paper/2401.12686/) (2024)
- [Robust Mean Field Social Control: A Unified Reinforcement Learning Framework](https://mlsanity.com/paper/2502.20029/) (2025)
- [Operator Learning for Families of Finite-State Mean-Field Games](https://mlsanity.com/paper/2602.13169/) (2026)
- [Learning in Stackelberg Mean Field Games: A Non-Asymptotic Analysis](https://mlsanity.com/paper/2509.15392/) (2025)
- [Bench-MFG: A Benchmark Suite for Learning in Stationary Mean Field Games](https://mlsanity.com/paper/2602.12517/) (2026)
- [Stationary Robust Mean-Field Games under Model Mismatches](https://mlsanity.com/paper/2606.22579/) (2026)
- [Neural Parameter Calibration for Finite-State Mean Field Games](https://mlsanity.com/paper/2606.23155/) (2026)

## Abstract (arXiv)

Motivated by models of epidemic control in large populations, we consider a Stackelberg mean field game model between a principal and a mean field of agents evolving on a finite state space. The agents play a non-cooperative game in which they can control their transition rates between states to minimize an individual cost. The principal can influence the resulting Nash equilibrium through incentives so as to optimize its own objective. We analyze this game using a probabilistic approach. We then propose an application to an epidemic model of SIR type in which the agents control their interaction rate and the principal is a regulator acting with non pharmaceutical interventions. To compute the solutions, we propose an innovative numerical approach based on Monte Carlo simulations and machine learning tools for stochastic optimization. We conclude with numerical experiments by illustrating the impact of the agents' and the regulator's optimal decisions in two models: a basic SIR model with semi-explicit solutions and a more complex model with a larger state space.