  We prove that large global systems of interacting (non necessarily similar)
dynamical units that are coupled by cooperative impulses, recurrently exhibit
the so called grand coalition, for which all the units arrive to their
respective goals simultaneously. We bound from above the waiting time until the
first grand coalition appears. Finally, we prove that if besides the units are
mutually similar, then the grand coalition is the unique subset of
goal-synchronized units that is recurrently shown by the global dynamics.
