  We study the problem of computing correlated strategies to commit to in games
with multiple leaders and followers. To the best of our knowledge, this problem
is widely unexplored so far, as the majority of the works in the literature
focus on games with a single leader and one or more followers. The fundamental
ingredient of our model is that a leader can decide whether to participate in
the commitment or to defect from it by taking on the role of follower. This
introduces a preliminary stage where, before the underlying game is played, the
leaders make their decisions to reach an agreement on the correlated strategy
to commit to. We distinguish three solution concepts on the basis of the
constraints that they enforce on the agreement reached by the leaders. Then, we
provide a comprehensive study of the properties of our solution concepts, in
terms of existence, relation with other solution concepts, and computational
complexity.
