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A proposal for non-simultaneous kidney exchange in pairs and chains and with deceased donors...

 Here's an ambitious proposal, that may face  obstacles to implementation, but which provides some clarity about the inefficiencies of current practice.

Unpaired Kidney Exchange: Overcoming Double Coincidence of Wants without Money

Mohammad Akbarpour, Julien Combe, Yinghua He, Victor Hiller, Robert Shimer, Olivier Tercieux

NBER Working Paper No. 27765, September 2020, pdf

Abstract: For an incompatible patient-donor pair, kidney exchanges often forbid receipt-before-donation (the patient receives a kidney before the donor donates) and donation-before-receipt, causing a double-coincidence-of-wants problem. Our proposed algorithm, the Unpaired kidney exchange algorithm, uses “memory” as a medium of exchange to eliminate these timing constraints. In a dynamic matching model, we prove that Unpaired delivers a waiting time of patients close to optimal and substantially shorter than currently utilized state-of-the-art algorithms. Using a rich administrative dataset from France, we show that Unpaired achieves a match rate of 57 percent and an average waiting time of 440 days. The (infeasible) optimal algorithm is only slightly better (58 percent and 425 days); state-of-the-art algorithms deliver less than 34 percent and more than 695 days. We draw similar conclusions from the simulations of two large U.S. platforms. Lastly, we propose a range of solutions that can address the potential practical concerns of Unpaired.

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