We study a class of sequential non-revelation mechanisms where hospitals make simultaneous take-it-or-leave-it oﬀers to doctors that either accept or reject them. We show that the mechanisms in this class are equivalent. They (weakly) implement the set of stable allocations in subgame perfect equilibrium. When all preferences are substitutable, the set of equilibria of the mechanisms in the class forms a lattice. Our results reveal a first-mover advantage absent in the model without contracts. We apply our findings to centralize school admissions problems, and we show obtaining pairwise stable allocations is possible through the immediate acceptance mechanism.
Economic Literature Classification Numbers: C78, D78.
Keywords: contracts, Many-to-many, ultimatum games.