  In this paper we consider multi-agent coalitional games with uncertain value
functions for which we establish distribution-free guarantees on the
probability of allocation stability, i.e., agents do not have incentives to
defect from the grand coalition to form subcoalitions for unseen realizations
of the uncertain parameter. In case the set of stable allocations, the so
called core of the game, is empty, we propose a randomized relaxation of the
core. We then show that those allocations that belong to this relaxed set can
be accompanied by stability guarantees in a probably approximately correct
fashion. Finally, numerical experiments corroborate our theoretical findings.
