To assign teachers to schools, a modified version of the well-known deferred acceptance mechanism has been proposed in the literature and is used in practice. We show that this mechanism fails to be fair and efficient for both teachers and schools. We identify a class of strategy-proof mechanisms that cannot be improved upon in terms of both efficiency and fairness. Using a rich dataset on teachers’ applications in France, we estimate teachers preferences and perform a counterfactual analysis. The results show that these mechanisms perform much better than the modified version of deferred acceptance. For instance, the number of teachers moving from their positions more than triples under our mechanism.
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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