We extend the standard analysis of decentralized markets to allow for the possibility that traders interact simultaneously with more than one trader on the opposite side of the market. In contrast with the literature, we reconcile the Walrasian equilibrium with the outcome of decentralized strategic trade: we show that there exist generic matching technologies that determine local market conditions such that, as market frictions vanish, the equilibrium price is the one that would result in the static Walrasian market. Our analysis highlights the importance of local market conditions for the determination of equilibrium prices.