Re-equilibration in Matching Markets with Contracts: Firm-Quasi-Stable Allocations

Yi-You Yang

Papers from arXiv.org

Abstract: We analyze the re-equilibration dynamics of matching markets with contracts following disruptions such as firm entry or worker exit. In a many-to-many framework with substitutable preferences, we identify firm-quasi-stable allocations as the canonical state space for out-of-equilibrium adjustment. We prove that this set forms a complete lattice and characterize stable allocations as the fixed points of a monotone Tarski operator defined on it, thereby establishing the lattice structure of stable allocations. We link this static characterization to dynamics by showing that decentralized vacancy chains approximate the centralized Tarski operator asynchronously. Specifically, we prove that the trajectory of a generalized firm-proposing deferred acceptance algorithm is bounded by the operator's iterations. This structural containment ensures both processes converge to the same limit. Consequently, the adjustment process exhibits order independence, with the final outcome invariant to the sequence of proposals. Finally, we derive welfare implications for market participants, and, under the law of aggregate demand, generalize the new-entrant advantage theorem to matching markets with contracts, establishing that entering firms achieve their optimal stable outcomes.

Date: 2023-05, Revised 2026-02
New Economics Papers: this item is included in nep-bec, nep-des and nep-mfd
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