  Current kidney exchange pools are of moderate size and thin, as they consist
of many highly sensitized patients. Creating a thicker pool can be done by
waiting for many pairs to arrive. We analyze a simple class of matching
algorithms that search periodically for allocations. We find that if only 2-way
cycles are conducted, in order to gain a significant amount of matches over the
online scenario (matching each time a new incompatible pair joins the pool) the
waiting period should be "very long". If 3-way cycles are also allowed we find
regimes in which waiting for a short period also increases the number of
matches considerably. Finally, a significant increase of matches can be
obtained by using even one non-simultaneous chain while still matching in an
online fashion. Our theoretical findings and data-driven computational
experiments lead to policy recommendations.
