Dr. Yongchao Zhang is currently an Associate Professor at School of Economics, Shanghai University of Finance and Economics. His current research interests include Mathematical Economics, Game Theory, and Matching Theory. His research has been published Journal of Economic Theory, Economic Theory, Economics Letters, Journal of Mathematical Economics, International Journal of Game Theory, Theoretical Economics, Advances in Mathematical Economics, Advances in Mathematics, among others.
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. 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.
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