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Complementarities and peer effects are common in matching markets, yet incorporating
them often leads to the nonexistence of stable matchings. We observe that matching is
often an ongoing process rather than a static allocation, where long-lived firms interact
over time with short-lived workers. We show that when wages are flexible and firms
are suffciently patient, a dynamically stable solution always exists in many-to-one
matching markets—even with complementarities and peer effects. Flexible wages are
crucial to our result, as they not only facilitate surplus extraction when firms cooperate
in no-poaching agreements but also enhance the threat of punishment through bidding
wars.
