We study decentralized trade in dynamic markets with homogeneous, non-atomic, buyers and sellers that wish to exchange one unit. In the first part of the paper we characterize equilibrium in a bargaining model with two-sided time varying outside options. In the second part we analyze a market equilibrium model in which (i) buyers and sellers are randomly matched in pairs; (ii) each buyer-seller pair bargains over the price of a good; and (iii) each agent has the option of abandoning negotiations, in which case the value of returning to the pool of unmatched agents constitutes an outside option. The second part is therefore an application of the first part in which the values of the outside options are endogenous to the model. Conditions for uniqueness of the market equilibrium are given; when it is unique it converges to the Walrasian outcome as frictions vanish. To the extent that multiplicity of market equilibria may (under some conditions) persist as frictions are removed, the limit of some sequences of equilibrium prices may converge to non-Walrasian values.