Essentially Stable Matchings

Many institutions that must assign a group of objects to a group of agents on the basis of priorities (also known as one-sided matching) desire the assignment to be stable, i.e., no agent should claim an object because she has higher priority than the agent to whom it is assigned. However, it is well-known that stable matchings are in general Pareto inefficient. This paper defines an assignment to be essentially stable if any claim an agent has to an object she prefers is vacuous, in the sense that it initiates a chain of reassignments that ultimately result in the initial claimant losing the object to a third student with even higher priority. We then show that an essentially stable and Pareto efficient assignment always exists, and can be found using Kesten’s efficiency adjusted deferred acceptance (EADA) algorithm. A main practical advantage to our definition is its simplicity: explaining to agents why their claims are vacuous becomes straightforward, which allows us to achieve efficiency while still adhering to the general principle that motivated stability in the first place. While our main application is to one-sided matching markets (such as school choice), our definition also has implications for two-sided markets, such as labor markets.