Altruistically Unbalanced Kidney Exchange
Although a pilot national live-donor kidney exchange program was recently launched in the US, the kidney shortage is increasing faster than ever. A new solution paradigm is able to incorporate compatible pairs in exchange. In this paper, we consider an exchange framework that has both compatible and in- compatible pairs, and patients are indifferent over compatible pairs. Only two-way exchanges are permitted due to institutional constraints. We explore the structure of Pareto-efficient matchings in this framework. The mathematical structure of this model turns out to be quite novel. We show that under Pareto-efficient matchings, the same number of patients receive transplants, and it is possible to construct Pareto-efficient matchings that match the same incompatible pairs while matching the least number of compatible pairs. We extend the celebrated Gallai-Edmonds Decomposition in the combinatorial optimization literature to our new framework. We also conduct comparative static exercises on how this decomposition changes as new compatible pairs join the pool.
|Date of creation:||01 Oct 2011|
|Date of revision:||30 Jun 2013|
|Contact details of provider:|| Postal: Boston College, 140 Commonwealth Avenue, Chestnut Hill MA 02467 USA|
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