In many-to-many matching markets with contracts and substitutable preferences, the re-equilibration map after population shocks is a join-semilattice homomorphism preserving the firm-optimal stable allocation and creating an opposition of interests between incumbent workers and firms.
Stability and Polarization of Interests in Job Ma tching,
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Decentralized Re-equilibration and Comparative Statics in Matching Markets with Contracts
In many-to-many matching markets with contracts and substitutable preferences, the re-equilibration map after population shocks is a join-semilattice homomorphism preserving the firm-optimal stable allocation and creating an opposition of interests between incumbent workers and firms.