Bargaining with binary private information

This paper studies bargaining between a seller and a buyer with binary private valuation. Because the setting is more tractable than the case of general valuation distributions (studied in Gul et al., 1986), we are able to explicitly construct the full set of equilibria via induction. This lets us provide a simple proof of the Coase conjecture and obtain new results: The seller extracts all surplus as she becomes more patient, and the equilibrium outcome converges to the perfect-information outcome as private information vanishes. We also fully characterize the case where there is a deadline: We establish that if the probability that the buyer's valuation is high is large enough, then the seller charges a high price at all times, there are trade bursts at the outset and the deadline, and trade occurs at a constant rate in between.