Reachable Stability Lattices after Population Shocks

Yi-You Yang

Papers from arXiv.org

Abstract: This paper studies how one-sided population shocks, such as worker exits and firm entries in senior-level labor markets, transform stability lattices in many-to-many matching markets with contracts and substitutable preferences. Deferred acceptance induces a re-equilibration map from the pre-shock to the post-shock stability lattice. We show that this map preserves order and joins, maps the pre-shock worker-optimal stable allocation to the greatest reachable element, and maps the pre-shock firm-optimal stable allocation to the post-shock firm-optimal stable allocation. Consequently, the reachable post-shock set forms a finite lattice. The construction factors through the firm-quasi-stable lattice, where the deferred-acceptance outcome coincides with the limit of a monotone Tarski-type operator. Sequential shock invariance shows that the reachable lattice is determined by the initial market and the aggregate shock, not by the order of exits and entries.

Date: 2023-05, Revised 2026-07
New Economics Papers: this item is included in nep-bec, nep-des and nep-mfd
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