# Optimization frameworks and sensitivity analysis of Stackelberg mean-field games

arXiv: https://arxiv.org/abs/2210.04110 · HTML: https://mlsanity.com/paper/2210.04110/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Oct 2022.

## Built on by (most cited first, 4 of 4)

- [MF-OML: Online Mean-Field Reinforcement Learning with Occupation Measures for Large Population Games](https://mlsanity.com/paper/2405.00282/) (2024)
- [MESOB: Balancing Equilibria & Social Optimality](https://mlsanity.com/paper/2307.07911/) (2023)
- [Learning in Stackelberg Mean Field Games: A Non-Asymptotic Analysis](https://mlsanity.com/paper/2509.15392/) (2025)
- [Learning Macroeconomic Policies through Dynamic Stackelberg Mean-Field Games](https://mlsanity.com/paper/2403.12093/) (2024)

## Abstract (arXiv)

This paper proposes and studies a class of discrete-time finite-time-horizon Stackelberg mean-field games, with one leader and an infinite number of identical and indistinguishable followers. In this game, the objective of the leader is to maximize her reward considering the worst-case cost over all possible ε-Nash equilibria among followers. A new analytical paradigm is established by showing the equivalence between this Stackelberg mean-field game and a minimax optimization problem. This optimization framework facilitates studying both analytically and numerically the set of Nash equilibria for the game; and leads to the sensitivity and the robustness analysis of the game value. In particular, when there is model uncertainty, the game value for the leader suffers non-vanishing sub-optimality as the perturbed model converges to the true model. In order to obtain a near-optimal solution, the leader needs to be more pessimistic with anticipation of model errors and adopts a relaxed version of the original Stackelberg game.