Integer programming for many-to-one stable matchings
Abstract
Matching markets have diverse applications, ranging from kidney transplantation to internship assignments. This talk focuses on many-to-one stable matching in the context of school choice. These are two-sided markets comprising students (children) and schools, which hold preferences and priorities, respectively, over one another. We begin by exploring classic game theory concepts that underpin these market-matching mechanisms, notably stability. Motivated by the Chilean school choice system, we use integer programming to model mechanisms that not only determine matchings between students and schools but also allocate additional seats to schools to optimize student welfare. Finally, we also discuss the use of integer programming to prioritize students with siblings and match them together.