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<p>We study a one-to-one matching market where the population is fixed. If some exogenous reason disrupts a worker-firm pair in a stable matching, can equilibrium in the market be restored? We present an algorithm that models this situation as a re-stabilization process involving a vacancy chain. Each step of the algorithm is a link of such a chain. We show that the length of this vacancy chain is intimately connected with the lattice structure of the set of stable matchings of the market. Namely, this length can be computed by considering the cardinalities of cycles in preferences derived from the initial and final stable matchings involved.</p>

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Counting steps for re-stabilization in a matching market with fixed population

  • 期刊论文

  • 发表日期：

    2026年2月2日

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  • Agustín G. Bonifacio,
  • Nadia Guiñazú,
  • Noelia Juarez,
  • Pablo Neme,
  • Jorge Oviedo

摘要

We study a one-to-one matching market where the population is fixed. If some exogenous reason disrupts a worker-firm pair in a stable matching, can equilibrium in the market be restored? We present an algorithm that models this situation as a re-stabilization process involving a vacancy chain. Each step of the algorithm is a link of such a chain. We show that the length of this vacancy chain is intimately connected with the lattice structure of the set of stable matchings of the market. Namely, this length can be computed by considering the cardinalities of cycles in preferences derived from the initial and final stable matchings involved.