Matching with Couples Revisited

It is well known that a stable matching in a many-to-one matching market with couples need not exist. We introduce a new matching algorithm for such markets and show that for a general class of large random markets the algorithm will find a stable matching with high probability. In particular we allow the number of couples to grow at a near-linear rate. Furthermore, truthtelling is an approximated equilibrium in the game induced by the new matching algorithm. Our results are tight: for markets in which the number of couples grows at a linear rate, we show that with constant probability no stable matching exists.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Itai Ashlagi, Mark Braverman, Avinatan Hassidim
• Keywords: CORR 2010, Education, Many-to-one Matching Market, Markets, Stable