Time horizons, lattice structures, and welfare in multi-period matching markets

We analyze a T-period, two-sided, one-to-one matching market without monetary transfers. Under natural restrictions on agents' preferences, which accommodate switching costs, status-quo bias, and other forms of inter-temporal complementarity, dynamically stable matchings exist. We propose a new ordering of the stable set ensuring that it forms a lattice. We investigate the robustness of dynamically stable matchings with respect to the market's time horizon and frequency of rematching opportunities.