Decentralized Re-equilibration and Comparative Statics in Matching Markets with Contracts

Yi-You Yang

Papers from arXiv.org

Abstract: Stable matching markets are subject to population disruptions such as worker exits or firm entries. This paper studies decentralized re-equilibration in many-to-many matching markets with contracts. The restriction of a pre-shock stable allocation to the surviving agents is firm-quasi-stable in the perturbed market. The set of firm-quasi-stable allocations forms a complete lattice under the worker-side Blair order. The firm-proposing deferred acceptance algorithm operates as an asynchronous iteration of a monotone operator on this lattice and restores stability. The induced re-equilibration map is a join-semilattice homomorphism that preserves joins under the worker-side Blair order and implies a cross-market opposition of interests: incumbent workers are weakly better off while incumbent firms are weakly worse off. Under the law of aggregate demand, the re-equilibration outcome admits an explicit algebraic representation: it is the join of the restricted pre-shock allocation and the firm-optimal stable allocation of the new market. Consequently, any entering firm receives exactly its firm-optimal assignment, independent of the pre-shock equilibrium selection.

Date: 2023-05, Revised 2026-04
New Economics Papers: this item is included in nep-bec, nep-des and nep-mfd
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