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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