Although a pilot national live-donor kidney exchange program was recently launched in the US, the kidney shortage is increasing faster than ever. A new solution paradigm is able to incorporate compatible pairs in exchange. In this paper, we consider an exchange framework that has both compatible...

Controlled choice over public schools attempts giving parents selection options while maintaining diversity of different student types. In practice, diversity constraints are often enforced by setting hard upper bounds and hard lower bounds for each student type. We demonstrate that, with hard...

We define the median stable matching for two-sided matching markets with wages and prove constructively that it exists.