Matching Markets with Couples Revisited

It is well known that a stable matching in a two-sided 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 grow in an ‘almost’ linear rate. Furthermore, the mechanism induced by the new algorithm is ‘almost’ incentive compatible. For markets in which the number of couples grow in a linear rate, we show that many ‘natural’ algorithms will not find a stable matching with constant probability.