  In this note, we introduce a distributed twist on the classic coupon
collector problem: a set of $m$ collectors wish to each obtain a set of $n$
coupons; for this, they can each sample coupons uniformly at random, but can
also meet in pairwise interactions, during which they can exchange coupons. By
doing so, they hope to reduce the number of coupons that must be sampled by
each collector in order to obtain a full set. This extension is natural when
considering real-world manifestations of the coupon collector phenomenon, and
has been remarked upon and studied empirically [Hayes and Hannigan 2006, Ahmad
et al. 2014, Delmarcelle 2019].
  We provide the first theoretical analysis for such a scenario. We find that
"coupon collecting with friends" can indeed significantly reduce the number of
coupons each collector must sample, and raises interesting connections to the
more traditional variants of the problem. While our analysis is in most cases
asymptotically tight, there are several open questions raised, regarding
finer-grained analysis of both "coupon collecting with friends", and of a
long-studied variant of the original problem in which a collector requires
multiple full sets of coupons.
