Efficient and Essentially Stable Assignments

An important desideratum in priority-based allocation is stability : no agent should claim an object because she has higher priority than the agent to whom it is assigned. However, stable matchings are in general Pareto inefficient, forcing upon designers a difficult trade-off. This paper alleviates this tension between efficiency and stability by defining 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 results in the initial claimant losing the object to a third student with even higher priority; on the other hand, if a non-vacuous claim exists, the assignment is strongly unstable. A main practical advantage to our definition is its simplicity: under an essentially stable assignment, explaining to agents why their claims are vacuous becomes straightforward, even to non-experts who may not fully understand the inner workings of a given mechanism. We show that mechanisms based on Shapley and Scarf’s TTC algorithm, while efficient, are strongly unstable, while Kesten’s EADA mechanism is both Pareto efficient and essentially stable. JEL Classification: C78, D61, D63, I20