Generalized Matching for School Choice

The school choice problem is formulated as a one-sided or a twosided matching problem. However, neither model adequately captures the features of the market design applications of school choice. In particular, the one-sided matching solution may be politically infeasible; and the two-sided matching solution may involve ine¢ ciencies. We introduce a generalized model that encompasses one-sided and two sided matching models and their hybrid. We propose a natural stability notion; characterize student optimal stable matchings; and provide a student optimal stable matching mechanism that reduces to the Top Trading Cycles algorithm when the problem is a one-sided matching problem and becomes equivalent to the Gale-Shapley student optimal stable matching algorithm when the problem is a two-sided matching problem.