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

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  • Yi-You Yang

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.

Suggested Citation

  • Yi-You Yang, 2023. "Decentralized Re-equilibration and Comparative Statics in Matching Markets with Contracts," Papers 2305.17948, arXiv.org, revised Apr 2026.
    • Handle: RePEc:arx:papers:2305.17948
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    References listed on IDEAS

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