# Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method

arXiv: https://arxiv.org/abs/2509.08161 · HTML: https://mlsanity.com/paper/2509.08161/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Sep 2025.

## Built on by (most cited first, 1 of 1)

- [Finite-Time Analysis of Q-Value Iteration for General-Sum Stackelberg Games](https://mlsanity.com/paper/2604.04394/) (2026)

## Abstract (arXiv)

In this work, we propose the first fully first-order method to compute an epsilon stationary Stackelberg equilibrium with convergence guarantees. To achieve this, we first reframe the leader follower interaction as single level constrained optimization. Second, we define the Lagrangian and show that it can approximate the leaders gradient in response to the equilibrium reached by followers with only first-order gradient evaluations. These findings suggest a fully first order algorithm that alternates between (i) approximating followers best responses through gradient descent and (ii) updating the leaders strategy via approximating the gradient using Lagrangian.