Separating equilibria in a continuous-time bargaining model with two-sided uncertainty

In this paper, we analyze the class of all smooth separating sequential equilibria in a continuous-time bargaining model with two-sided uncertainty. Trade between players occurs whenever there is surplus to be shared and delay is used to signal their valuations. When the buyer and the seller have a common discount rate, we show that the final outcome is unique among all these equilibria: the difference between the highest possible buyer's valuation and the lowest possible seller's valuation always narrows down at a rate exactly equal to the discount rate. When their discount rates differ, the more patient side always reveals his valuation first in the unique smooth separating equilibrium.