Time Horizons, Lattice Structures, and Welfare in Multi-Period Matching Markets

We analyze a T-period, bilateral matching economy 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 an ordering of the set of dynamically stable matchings ensuring this set forms a lattice. We investigate the robustness of dynamically stable matchings with respect to the market’s time horizon. We relate our analysis to market-design applications, including student-school assignment and labor markets.