Price setting in a decentralized market and the competitive outcome

This paper studies a decentralized, dynamic matching and bargaining market: buyers and sellers are matched into pairs. Traders exit the market at a constant rate, inducing search costs (frictions). All price offers are made by sellers. Despite the fact that sellers have all the bargaining power we show that they set competitive prices in the limit when frictions become small. Previous literature has restricted the sellers' bargaining power. We dispense with this restriction and show that the convergence result does not depend on the distribution of bargaining power. Our model allows us to isolate basic market clearing forces that ensure the competitive outcome in the frictionless limit. For the particular case of homogeneous sellers we characterize the equilibrium price by the familiar Lerner formula. We use this formula to provide comparative static results of the decentralized trading outcome with respect to the level of the search frictions.