  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.
