An alternative characterization of the deferred acceptance algorithm

Kojima and Manea (2010) present two characterizations of when an allocation rule corresponds to the agent‐proposing deferred acceptance (DA) algorithm for some substitutable priority rule of the objects being assigned. Building on their results we characterize when an allocation rule is outcome equivalent to the DA algorithm for every substitutable priority rule. In particular, an assignment rule satisfies mutual best (MB) if an agent is always assigned her most preferred object whenever she has the highest priority for it. This mild requirement is a necessary but far from sufficient condition for an assignment rule to be stable. We demonstrate that any allocation mechanism that satisfies MB along with non‐wastefulness, population monotonicity and either individually rational monotonicity or weak Maskin monotonicity not only is a stable assignment mechanism but is equivalent to the agent proposing DA algorithm.