We develop a model of matching with contracts which incorporates, as special cases, the college admissions problem, the Kelso-Crawford labor market matching model, and ascending package auctions. We introduce a new "law of aggregate demand" for the case of discrete heterogeneous workers and show that, when workers are substitutes, this law is satisfied by profit-maximizing firms. When workers are substitutes and the law is satisfied, truthful reporting is a dominant strategy for workers in a worker-offering auction/matching algorithm. We also parameterize a large class of preferences satisfying the two conditions.
Hatfield, John William and Paul R. Milgrom.
2005."Matching with Contracts."American Economic Review,
95(4): 913-935.DOI: 10.1257/0002828054825466