Matching with Contracts

Abstract

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.

Group incentive compatibility for matching with contracts

“…Under the substitutes condition, the law of aggregate demand is essentially the weakest possible sufficient condition for group strategy-proofness (or even strategy-proofness). 2 The many previous results on strategy-proofness and group strategy-proofness (Dubins and Freedman, 1981;Roth, 1982;Martinez et al, 2004;Abdulkadiroglu, 2005;Hatfield and Milgrom, 2005) are special cases of this result. Furthermore, it is well-known that for the doctor-optimal stable mechanism a group of doctors can deviate in such a way to make some members strictly better off and none worse off (Dubins and Freedman, 1981) and that the mechanism is not even strategy-proof for hospitals (Roth, 1982).…”

“…The medical residency matching mechanism in the U.S. (National Residency Matching Program) and student assignment systems in New York City and Boston (among others) are examples of mechanisms designed by economists using the theory. 1 Hatfield and Milgrom (2005) present a unified framework of matching with contracts, which includes the two-sided matching models and package auction models as special cases. They introduce the substitutes condition of contracts, which generalizes the substitutability condition in the matching literature (Roth and Sotomayor, 1990).…”

Strategy-Proofness Makes the Difference: Deferred-Acceptance with Responsive Priorities

“…It is exactly this responsiveness-to-individual-priorities feature that makes the agent-proposing deferred-acceptance mechanism easily applicable in practice (Roth, 2008). Kojima and Manea (2010) provide two characterizations of deferred acceptance mechanisms with so-called acceptant substitutable priorities (a larger class of mechanisms than the class of responsive DA-mechanisms which is based on priorities that are determined by a choice function that reflects substitutability in priorities over sets of agents; see also Hatfield and Milgrom, 2005 …”

“…In contrast, Kojima and Manea (2010) characterize the class of DA-mechanisms with so-called acceptant substitutable priorities: a larger class of mechanisms than the class of responsive DA-mechanisms that is based on priorities that are determined by a choice function that reflects substitutability in preferences over sets of agents (see also Hatfield and Milgrom, 2005).…”

Strategic Models of Intermediation Networks

“…These conditions generalize the gross-substitute condition in Kelso and Crawford (1982). Insights of two-sided matching theory-e.g., Adachi (2000) and Hatfield and Milgrom (2005)-generalize besides existence: stable outcomes represent a lattice in the payoff space of firms at the top of the network-i.e., suppliers-and firms at the bottom-i.e., consumers. The generality of the model does not allow, though, to derive specific insights into the effect of the network structure on outcomes.…”