A theory of stability in dynamic matching markets
I study dynamic matching markets where matching opportunities arrive over time, matching is one-to-one and irreversible. I propose a stability notion, dynamic stability, which accommodates the trade-off between matching and waiting for a better match. Dynamically stable matchings may fail to exist in two-sided economies; however, they always exist in one-sided economies. The non-existence result reveals a new form of unraveling in matching markets, whereby agents wish to delay the time at which they are matched. These findings rationalize why clearing houses in different markets deal differently with agents who reject a current offer to wait for a better match.
Keywords: matching, dynamic matching, stability, core, one-stage deviation principle, market design, unraveling, organ donation, public housing, child adoption