Bilateral Matching and Bargaining with Private Information

We study a steady state of the market with inflowing cohorts of buyers and sellers. The traders are randomly matched pairwise driven by a Pissarides-style matching function. Two bargaining protocols are considered: random offering and the k-double auction. There are frictions due to time discounting and costly participation. We derive a necessary and sufficient condition for existence of equilibrium with trade. Two types of equilibria are shown to exist: those in which each meeting results in a trade, and those in which some meetings do not. If the random-offering protocol is used, all equilibria converge at the linear rate to the Walrasian outcome as the frictions vanish. Under the k-double auction protocol, however, there also non-convergent equilibria.