We study dynamic matching without money
when one side of the market is dynamic with arrivals and de-
partures and the other is static and agents have strict prefer-
ences over agents on the other side of the market. In enabling
stability properties, so that no pair of agents can usefully devi-
ate 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.