Uncertainty about Uncertainty and Delay in Bargaining

We study a one-sided offers bargaining game in which the buyer has private information about the value of the object and the seller has private infromation about his beliefs about the buyer. We show that this uncertainty about uncertainties dramatically changes the set of possible outcomes when compared to two-sided private information. In particular, higher order beliefs can lead to a dalay in reaching agreement even when the seller makes frequent offers, while in the case of two-sided first order private information, agreement is reached almost instantly. Furthermore, we show that not all types of higher order beliefs lead to a delay: the crucial condition is that when uncertain about uncertainties, one assigns positive probability to certainty.