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.

翻译：许多真实世界的战略游戏都涉及多个玩家之间的互动。 我们研究一个等级化的多玩家游戏结构, 使角色不对称的玩家可以分为领导者和追随者, 一种常被称作 Stackelberg 游戏或追随者游戏的游戏。 特别是, 我们侧重于一个有多重领导者和单一追随者参加的Stackelberg 游戏场景, 叫做 MLSF 游戏, 叫做 MLSF 游戏, 我们为 MLSF 游戏提出了一个新的不对称平衡概念, 叫做 Cor 相关Stackelberg Equiblium (CSE) 。 我们设计了在线学习算法, 使玩家能够以分散的方式互动, 并证明它能够实现无外部 Stakkelberg- regret 学习。 这进一步转化了通过将无外悔减为无反感。 在我们工作的核心, 我们通过平衡不同学习结构的探索和开发, 来解决如何在追领者游戏中学习平衡, 使用吵的乐队回馈的问题错综复杂。