  Walrasian prices, if they exist, have the property that one can assign every
buyer some bundle in her demand set, such that the resulting assignment will
maximize social welfare. Unfortunately, this assumes carefully breaking ties
amongst different bundles in the buyer demand set. Presumably, the shopkeeper
cleverly convinces the buyer to break ties in a manner consistent with
maximizing social welfare. Lacking such a shopkeeper, if buyers arrive
sequentially and simply choose some arbitrary bundle in their demand set, the
social welfare may be arbitrarily bad. In the context of matching markets, we
show how to compute dynamic prices, based upon the current inventory, that
guarantee that social welfare is maximized. Such prices are set without knowing
the identity of the next buyer to arrive. We also show that this is impossible
in general (e.g., for coverage valuations), but consider other scenarios where
this can be done. We further extend our results to Bayesian and bounded
rationality models.
