Thoughts on kidney exchange in a steady state

As kidney exchange grows, a growing number of people are thinking about how it might be organized. We can welcome to the club Larry Ausubel and Thayer Morrill, two economists with varied interests in market design, whose paper Sequential Kidney Exchange explores how non-simultaneous chains might look in a steady state world, in which the composition of the pool of patient-donor pairs would be completely stable over time. Under that assumption, an exchange that could be conducted simultaneously today, could also be conducted over multiple days, in which a pair would first donate a kidney, and then receive one from another pair (just like the one that was available today) tomorrow.

"Abstract: The literature on kidney exchange considers situations where two or more patients needing transplants have live donors volunteering to donate one of their kidneys, but the donated organs are incompatible with the respective patients. The traditional analysis assumes that all components of the live donor exchange must occur simultaneously. People cannot write enforceable contracts that commit them to donate their organs; consequently, incentive compatibility is obtained by trading simultaneously. Unfortunately, a two-way exchange then requires the simultaneous availability of four operating rooms and associated personnel, while a three-way exchange requires six operating rooms, etc. The requirement of four or more operating rooms for concurrent surgeries may pose a significant constraint on the beneficial exchanges that may be attained. The basic insight of this paper is that satisfaction of the incentive constraint does not require simultaneous exchange; rather, it requires that organ donation occurs no later than the associated organ receipt. Using sequential exchanges may relax the operating-room constraint and thereby increase the number of beneficial exchanges. We show that most benefits of sequential exchange can be accomplished with only two concurrent operating rooms."

Note that Ausubel and Morrill propose to solve the incentive problem by having each patient-donor pair donate a kidney before (or at least no later than) they receive one, so reneging is not an issue. This is very different than current practice in non-simultaneous chains, which is to insure the individual rationality of the outcome by  having each pair receive a kidney before donating one. This latter approach means that non-simultaneous chains can only happen when initiated by a non-directed donor (a severe limitation). In the model Ausubel and Morrill explore, the danger that some pair won't receive a kidney after giving one vanishes because, in the steady state, a pair of the right kind will always be available.

Kidney exchange is a field in which ideas that aren't ready for implementation when published sometimes find an echo in practice pretty fast. (It wasn't long ago that only exchanges between two pairs were being done. But integrating chains with exchanges which had been proposed earlier, happened pretty fast thereafter.) I already know of some non-simultaneous chains in which a pair has donated a kidney before receiving one, for logistical reasons, after the full chain has already been identified. Those chains always make me feel a little nervous, but maybe they will become more common as the risks and rewards become better understood.