Choice and Matching

Abstract

We study path-independent choice rules applied to a matching context. We use a classic representation of these choice rules to introduce a powerful technique for matching theory. Using this technique, we provide a deferred acceptance algorithm for many-to-many matching markets with contracts and study its properties. Next, we obtain a compelling comparative static result: If one agent's choice expands, the remaining agents on her side of the market are made worse off, while agents on the other side of the market are made better off. We study the impact of firm mergers using this result.

A choice rule with a capacity that always binds whenever possible is deemed acceptant. We provide a constructive proof to show that every path-independent choice rule has an acceptant path-independent expansion with the same maximum cardinality. Finally, we characterize the class of responsive choice rules using acceptance.

Keywords: Two-Sided Matching, Choice Function, Acceptance, Path Independence, Stability

JEL Classification: C78, D47, D71, D78