We extend the standard analysis of decentralized markets to allow for the p
ossibility that traders interact simultaneously with more than one trader o
n the opposite side of the market. In contrast with the literature, we reco
ncile the Walrasian equilibrium with the outcome of decentralized strategic
trade: we show that there exist generic matching technologies that determi
ne local market conditions such that, as market frictions vanish, the equil
ibrium price is the one that would result in the static Walrasian market. O
ur analysis highlights the importance of local market conditions for the de
termination of equilibrium prices.