How to Find a Stable and Efficient Matching for Weak Priorities via Strategy-Proof Rules

Abstract

We consider a priority based allocation problem with general weak priorities. We focus on two strategy-proof mechanisms: the deferred acceptance (DA) mechanism and the top trading cycles (TTC) mechanism. We give two conditions on weak priority structures whereby each of the DA mechanism and TTC mechanism with an arbitrarily fixed tie-breaking rule is stable and efficient. Our conditions are a generalization of each of Ergin (2002) 's and Kesten (2006)'s conditions about strict priorities. Our two conditions do not imply each other, whereas it is known that Kesten's condition implies Ergin's condition. Our analysis shows that a strategy-proof selection from stable and efficient matchings can be done for a larger domain of priority structures than the domain of Ehlers and Erdil (2010).