A matching and bargaining model in a market with one seller and two buyers, differing only in their reservation price, is analyzed. No subgame perfect equilibrium exists for stationary strategies. We demonstrate the existence of inefficient equilibria in which the low buyer receives the good with large probability, even as friction becomes negligible. We investigate the relationship between the use of Nash and sequential bargaining. Nash bargaining seems applicable only when the sequential approach yields a unique stationary strategy subgame perfect equilibrium