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.
Smart Lotteries in School Choice: Ex-ante Pareto-Improvement with Ex-post Stability
UNSW Sydney（新南威尔士大学）；ELTE Centre for Economic and Regional Studies（布达佩斯经济区域研究中心）；Department of Quantitative Economics, Maastricht University（马斯特里赫特大学数量经济学系）；HUN-REN Institute for Computer Science and Control（匈牙利科学院计算机与控制研究所）；Budapest University of Technology and Economics（布达佩斯技术与经济大学）
Jacobs Technion-Cornell Institute, Cornell Tech（康奈尔科技 Jacobs 学院）；School of Management, The University of Texas at Dallas（德克萨斯大学达拉斯分校管理学院）；CDSES, Cornell University（康奈尔大学）
