2021/09/19 by Hugo Gimbert, Gimbert, Hugo, Claire Mathieu +3
Economics, Econometrics and Finance · Social Sciences · #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Economics and business #Game Theory and Voting Systems #Local Government Finance and Decentralization #Theoretical Economics (econ.TH)
paper · pdf · doi:10.48550/arxiv.2109.09089
openalex publication_date 2021/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
School choice is the two-sided matching market where students (on one side) are to be matched with schools (on the other side) based on their mutual preferences. The classical algorithm to solve this problem is the celebrated deferred acceptance procedure, proposed by Gale and Shapley. After both sides have revealed their mutual preferences, the algorithm computes an optimal stable matching. Most often in practice, notably when the process is implemented by a national clearinghouse and thousands of schools enter the market, there is a quota on the number of applications that a student can submit: students have to perform a partial revelation of their preferences, based on partial information on the market. We model this situation by drawing each student type from a publicly known distribution and study Nash equilibria of the corresponding Bayesian game. We focus on symmetric equilibria, in which all students play the same strategy. We show existence of these equilibria in the general case, and provide two algorithms to compute such equilibria under additional assumptions, including the case where schools have identical preferences over students.