Skip to content # The Roommate Game: An Exploration of Stable Matchings

## Activity Guide

# This guide looks at the activity in detail and goes into the underlying math.

Bolognese, Chris. Dennett, Emily. (2020). The Roommate Game: An Exploration of Stable Matchings. In S. Bowen (Ed.), Math Circle Activity Database. American Institute of Mathematics. https://mathcircles.org/activity/the-roommate-game

Contributor(s): Chris Bolognese, Emily Dennett

Math Circles: Columbus Math Teachersâ€™ Circle, MTC Network

- Activity Description
- Topics Covered
- Session Styles
- Mathematical Practices

College students need to be matched with a roommate. They each make a list of who they prefer to room with. Given the preference lists for each individual, can we find a matching that is stable? That is, would any pair ask to change rooms because they would rather room together than with their current roommates? Explorations lead to new questions or new avenues to investigate using various mathematical methods including, but not limited to, combinatorics, graph theory, or matrices.