Constrained School Choice with Incomplete Information

TL;DR

This paper studies how students and schools can reach stable matchings when students have limited information and must strategize under incomplete preferences, extending classical school choice models.

Contribution

It introduces a Bayesian game framework for constrained school choice with incomplete information and proves the existence of symmetric Nash equilibria, along with algorithms to compute them.

Findings

Existence of symmetric Nash equilibria in the model.

Algorithms for computing equilibria under certain assumptions.

Analysis of equilibrium properties in incomplete information settings.

Abstract

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.