Erratum to: Chinese College Admissions and School Choice Reforms: A Theoretical Analysis (Journal of Political Economy)

Abstract

By definition, if mechanism Je is more manipulable than mechanism J,e0 then any truth-telling Nash equilibrium (where all students report their true preferences) of Je is also a Nash equilibrium of J . Therefore, corollary 2 (which is implied by theorem 1) in the paper “Chinese College Ad-e0 missions and School Choice Reforms: A Theoretical Analysis,” published in the February 2017 issue of the Journal of Political Economy (vol. 125 (1)), is incorrect. Equilibrium comparisons in corollary 2 hold under truth telling. The corrected statement of corollary 2 is as follows. Corollary 2. Any truth-telling Nash equilibrium of the preference revelation game associated with Je is also a Nash equilibrium of that of Je0 where e0 > e. Similarly, equilibrium comparisons in theorem 2 and its extension theorem 5, which invoke corollary 2, hold under truth telling. The corrected statement of theorem 2 is as follows. Theorem 2. Let e0 = ke for some k ∈ N ⋃f∞g. Any truth-telling equilibrium of Je that leads to a stable matching is also an equilibrium of J ande0 leads to the same stable matching. However, the converse is not true; that is, there are stable truth-telling equilibria of J that neither may be equilibriae0 nor may be stable under Je. With this modification, the converse statement in theorem 2 (and in its extension theorem 5) still holds and can easily be shown by adding an extra student (who prefers school se 0 most but has the lowest priority at all schools) and an extra school (which is the least preferred by all stu-dents) to the example in the original proof. We regret the error. We thank Kentaro Tomoeda for pointing out the error in corollary 2.