Matching and market design in the January issue of Theoretical Economics

 The current issue has three papers on the market design of matching markets.

Theoretical Economics, Volume 17, Number 1 (January 2022): Table of Contents

Here are the market design articles that caught my eye:

Rank-optimal assignments in uniform markets  by Afshin Nikzad

"We prove that in a market where agents rank objects independently and uniformly at random, there exists an assignment of objects to agents with a constant average rank (i.e., an average rank independent of the market size). The proof builds on techniques from random graph theory and the FKG inequality (Fortuin et al. (1971)). When the agents’ rankings are their private information, no Dominant Strategy Incentive Compatible mechanism can implement the assignment with the smallest average rank; however, we show that there exists a Bayesian Incentive Compatible mechanism that does so. Together with the fact that the average rank under the Random Serial Dictatorship (RSD) mechanism grows infinitely large with the market size, our findings indicate that the average rank under RSD can take a heavy toll compared to the first-best, and highlight the possibility of using other assignment methods in scenarios where average rank is a relevant objective.

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Family ties: school assignment with siblings by Umut Dur, Thayer Morrill, and William Phan

"We introduce a generalization of the school choice problem motivated by the following observations: students are assigned to grades within schools, many students have siblings who are applying as well, and school districts commonly guarantee that siblings will attend the same school. This last condition disqualifies the standard approach of considering grades independently as it may separate siblings. We argue that the central criterion in school choice—elimination of justified envy—is now inadequate as it does not consider siblings. We propose a new solution concept, suitability, that addresses this concern, and we introduce a new family of strategy-proof mechanisms where each satisfies it. Using data from the Wake County magnet school assignment, we demonstrate the impact on families of our proposed mechanism versus the “naive” assignment where sibling constraints are not taken into account."

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Optimal organ allocation policy under blood-type barriers with the donor-priority rule by Jaehong Kim and Mengling Li

"Shortages in organs for transplantation have resulted in a renewed interest in designing incentive policies to promote organ supply. The donor-priority rule, which grants priority for transplantation based on deceased organ donor registration status, has proven to be effective in both theory and practice. This study investigates the implications of the donor-priority rule for optimal deceased organ allocation policy design under a general formulation of blood-type barriers. We find that for any blood typing and organ matching technology, reserving type X organs for only type X patients maximizes the aggregate donation rate under regular distributions, which also ensures equity in organ sharing. Moreover, this is the unique optimal allocation policy if and only if the directed compatibility graph that corresponds to a given organ matching technology is acyclic."