A dynamic trading game is examined in which two uninformed buyers engage in Bertrand-like competition to attempt to purchase a single object of uncertain quality from an informed seller. It is shown that there exists a unique perfect sequential equilibrium. The game is compared to an analogous bargaining game in which a single uninformed buyer makes offers to a single seller. Despite the fact that in the equilibrium of the competitive game, buyers compete away their surplus, it is shown that sellers can often gain a higher ex ante surplus in the bargaining game.