Abstract
We propose and analyze modular stable matching rules as a candidate for a foundational framework to address issues of social welfare and equity in the stable matching model. We present two characterizations for modular stable matching rules that reveal the ordinal content of optimizing a modular function under the stability constraint, and present several examples. Then, we propose a new equity notion and characterize the class of modular stable matching rules that comply with this notion. Our analysis indicates that modular matching rules are both structured and rich enough to implement a wide range of objectives.