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. Key words: Bargaining, signaling, delay, two-sided uncertainty.

The formal theory of bargaining originated with John Nash's work in the early 1950s. This book discusses two recent developments in this theory. The first uses the tool of extensive games to construct theories of bargaining in which time is modeled explicitly. The second applies the theory of bargaining to the study of decentralized markets. Rather than surveying the field, the authors present a select number of models, each of which illustrates a key point. In addition, they give detailed proofs throughout the book.