Weak Stability and Pareto Efficiency in School Choice
33 Pages Posted: 31 May 2017 Last revised: 28 Nov 2017
Date Written: September 1, 2017
We propose a new notion of weak stability for two-sided matching problems. A matching is said to be weakly stable if none of its blocking pairs can be matched by a more stable matching—one with a weakly smaller set of blocking pairs. We then apply this concept to school choice and study its compatibility with the Pareto efficiency of students’ assignments. A matching is said to be self-constrained efficient if it is not Pareto dominated by any matching more stable than it. We prove that the following are equivalent for a matching: (i) it is weakly stable and self-constrained efficient; (ii) it is exactly the outcome of the generalized Kesten’s efficiency-adjusted deferred acceptance mechanism which uses its own set of blocking pairs as consenting constraint; and (iii) it weakly Pareto dominates all matchings more stable than it.
Keywords: Deferred acceptance algorithm, Pareto efficiency, school choice, stability, weak stability
JEL Classification: C78; D61; D78; I20
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