Matching markets such as day care, student exchange, refugee resettlement, and couples problems involve agents of different sizes, that is agents who require different amounts of capacity. I study a matching market between agents and objects where the size of an agent is either one or two. Contrary to canonical models, the set of stable matchings may be empty. I identify a trade-off for existence: it is always possible to either bound the instability to a certain number of units per object or to eliminate waste but the existence of a matching that does both is not guaranteed. I develop two fairness criteria that lie on either side of this trade-off: unit-stability bounds the instability and size-stability eliminates waste. I show that size-stability is more desirable than unit-stability from a welfare point of view.

Link to paper: daviddelacretaz.net/wp-content/uploads/2019/01/DDelacretaz-SMMS-Jan19.pdf