# Learning Correlated Stackelberg Equilibrium in General-Sum Multi-Leader-Single-Follower Games

arXiv: https://arxiv.org/abs/2210.12470 · HTML: https://mlsanity.com/paper/2210.12470/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 40 references that are in the map.
- First posted on arXiv 22 Oct 2022.

## Builds on (most cited first, 4 of 4)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Online Learning: A Modern Introduction Using Convex Optimization](https://mlsanity.com/paper/1912.13213/) (2019)
- [Optimization, Learning, and Games with Predictable Sequences](https://mlsanity.com/paper/1311.1869/) (2013)
- [Sample-Efficient Learning of Stackelberg Equilibria in General-Sum Games](https://mlsanity.com/paper/2102.11494/) (2021)

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

- [Online Learning in Stackelberg Games with an Omniscient Follower](https://mlsanity.com/paper/2301.11518/) (2023)
- [Optimal Cooperative Multiplayer Learning Bandits with Noisy Rewards and No Communication](https://mlsanity.com/paper/2311.06210/) (2023)
- [Decentralized Online Learning in General-Sum Stackelberg Games](https://mlsanity.com/paper/2405.03158/) (2024)
- [Finite-Time Analysis of Q-Value Iteration for General-Sum Stackelberg Games](https://mlsanity.com/paper/2604.04394/) (2026)

## Abstract (arXiv)

Many real-world strategic games involve interactions between multiple players. We study a hierarchical multi-player game structure, where players with asymmetric roles can be separated into leaders and followers, a setting often referred to as Stackelberg game or leader-follower game. In particular, we focus on a Stackelberg game scenario where there are multiple leaders and a single follower, called the Multi-Leader-Single-Follower (MLSF) game. We propose a novel asymmetric equilibrium concept for the MLSF game called Correlated Stackelberg Equilibrium (CSE). We design online learning algorithms that enable the players to interact in a distributed manner, and prove that it can achieve no-external Stackelberg-regret learning. This further translates to the convergence to approximate CSE via a reduction from no-external regret to no-swap regret. At the core of our works, we solve the intricate problem of how to learn equilibrium in leader-follower games with noisy bandit feedback by balancing exploration and exploitation in different learning structures.