Transparency of outside options in bargaining

We study the effect of the transparency of outside options in bilateral bargaining. A seller posts prices to screen a buyer over time, and the buyer may receive an outside option at a random time. We consider two information regimes: one in which the arrival of the outside option is public and one in which the arrival is private. A public arrival of the outside option works as a commitment device that forces the buyer to opt out immediately. This effect leads to a generically unique equilibrium in which the Coase conjecture holds. In contrast, a private arrival of the outside option may lead to additional delay and equilibrium multiplicity. The Coase conjecture fails in some equilibria. The buyer's preference about transparency is time-inconsistent: she prefers to commit to making arrivals public, but she is unwilling to disclose her outside option after the arrival. Moreover, the seller benefits from having the buyer privately observe her outside option.