Outside Options, Reputations, and the Partial Success of the Coase Conjecture

A buyer and seller bargain in continuous time over a good. Bargainers can be rational or committed to some fixed price. A rational buyer has a private value and outside option. If the set of buyer values and commitment types is rich and the probability of commitment vanishes, outcomes are partially consistent with the Coase conjecture: the seller chooses a price below the maximum of the lowest outside option and half the lowest value; the buyer immediately accepts or takes his outside option.