We study dynamic matching without money when one side of the market is dynamic with arrivals and departures and the other is static and agents have strict preferences over agents on the other side of the market. In enabling stability properties, so that no pair of agents can usefully deviate from the match, we consider the use of a fall-back option where the dynamic agents can be matched, if needed, with a limited number of agents from a separate "reserve" pool. We introduce the GSODAS mechanism, which is truthful for agents on the static side of the market and stable. In simulations, we establish that GSODAS dominates in rank-efficiency a pair of randomized mechanisms that operate without the use of a fall-back option. In addition, we demonstrate good rank-efficiency in comparison to a non-truthful mechanism that employs online stochastic optimization.
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