  Multi-agent reinforcement learning (MARL) problems are challenging due to
information asymmetry. To overcome this challenge, existing methods often
require high level of coordination or communication between the agents. We
consider two-agent multi-armed bandits (MABs) and Markov decision processes
(MDPs) with a hierarchical information structure arising in applications, which
we exploit to propose simpler and more efficient algorithms that require no
coordination or communication. In the structure, in each step the ``leader"
chooses her action first, and then the ``follower" decides his action after
observing the leader's action. The two agents observe the same reward (and the
same state transition in the MDP setting) that depends on their joint action.
For the bandit setting, we propose a hierarchical bandit algorithm that
achieves a near-optimal gap-independent regret of
$\widetilde{\mathcal{O}}(\sqrt{ABT})$ and a near-optimal gap-dependent regret
of $\mathcal{O}(\log(T))$, where $A$ and $B$ are the numbers of actions of the
leader and the follower, respectively, and $T$ is the number of steps. We
further extend to the case of multiple followers and the case with a deep
hierarchy, where we both obtain near-optimal regret bounds. For the MDP
setting, we obtain $\widetilde{\mathcal{O}}(\sqrt{H^7S^2ABT})$ regret, where
$H$ is the number of steps per episode, $S$ is the number of states, $T$ is the
number of episodes. This matches the existing lower bound in terms of $A, B$,
and $T$.
