Matching With Minimal Priority Rights

I study two prominent strategyproof matching rules when strict priorities over objects are given exogenously: the Deferred Acceptance Rule (DA) and the Top Trading Cycle Rule With Inheritance (TTC). It is well known that the DA rule is stable while the TTC rule is efficient, but not vice versa, and that these two properties cannot be reconciled. The primary innovation of the paper is the introduction of a new weaker concept of stability, Individual Trade Stability, which allows for trading the priorities for objects, a property that is satisfied by both the DA and TTC rules, as well as by all the hybrid rules of these two matching rules that I propose, called Deferred Trading Cycle Rules. The main result is a characterization of the class of Deferred Trading Cycle Rules by Individual Trade Stability, Constrained Efficiency, and an invariance property called Lower Invariance. The characterized class of matching rules include the DA and TTC rules as the two extreme rules in the class. ∗Department of Economics, Concordia University and CIREQ, 1455 de Maisonneuve Blvd. West, Montreal, Quebec H3G 1M8, Canada; e-mail: [email protected] †I would like to thank Justin Leroux, Jim Schummer, Utku Ünver, and Licun Xue for comments and discussions. Financial support from the Canada Research Chair fund is greatly appreciated.