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Auctions, Matching and the Law of Aggregate Demand

Jan 2004
Working Paper
03-008
By  John Hatfield, Paul Milgrom
We develop a model of matching with contracts which has, 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, the law is satisfied by the demands of 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.