  In barter exchanges, participants swap goods with one another without
exchanging money; exchanges are often facilitated by a central clearinghouse,
with the goal of maximizing the aggregate quality (or number) of swaps. Barter
exchanges are subject to many forms of uncertainty--in participant preferences,
the feasibility and quality of various swaps, and so on. Our work is motivated
by kidney exchange, a real-world barter market in which patients in need of a
kidney transplant swap their willing living donors, in order to find a better
match. Modern exchanges include 2- and 3-way swaps, making the kidney exchange
clearing problem NP-hard. Planned transplants often fail for a variety of
reasons--if the donor organ is refused by the recipient's medical team, or if
the donor and recipient are found to be medically incompatible. Due to 2- and
3-way swaps, failed transplants can "cascade" through an exchange; one US-based
exchange estimated that about 85% of planned transplants failed in 2019. Many
optimization-based approaches have been designed to avoid these failures;
however most exchanges cannot implement these methods due to legal and policy
constraints. Instead we consider a setting where exchanges can query the
preferences of certain donors and recipients--asking whether they would accept
a particular transplant. We characterize this as a two-stage decision problem,
in which the exchange program (a) queries a small number of transplants before
committing to a matching, and (b) constructs a matching according to fixed
policy. We show that selecting these edges is a challenging combinatorial
problem, which is non-monotonic and non-submodular, in addition to being
NP-hard. We propose both a greedy heuristic and a Monte Carlo tree search,
which outperforms previous approaches, using experiments on both synthetic data
and real kidney exchange data from the United Network for Organ Sharing.
