This paper considers a market where pairs of agents who are interested in carrying out a transaction are brought together by a stochastic process and, upon meeting, initiate a bargaining process over the terms of the transaction. The basic bargaining problem is treated with the strategic approach. The paper derives the steady state equilibrium agreements; analyzes their dependence on market conditions such as the relative numbers of agents of different types; and discusses their relations with the competitive equilibrium outcome and other results in the search equilibrium literature.