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

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