A seller and a buyer bargain over the terms of trade for an object. The seller receives a perfect signal that determines the value of the object to both players, whereas the buyer remains uninformed. We analyze the infinite‐horizon bargaining game in which the buyer makes all the offers. When the static incentive constraints permit first‐best efficiency, then under some regularity conditions the outcome of the sequential bargaining game becomes arbitrarily efficient as bargaining frictions vanish. When the static incentive constraints preclude first‐best efficiency, the limiting bargaining outcome is not second‐best efficient and may even perform worse than the outcome from the one‐period bargaining game. With frequent buyer offers, the outcome is then characterized by recurring bursts of high probability of agreement, followed by long periods of delay in which the probability of agreement is negligible.