Bargaining While Learning About New Arrivals, Second Version

We study dynamic bargaining with uncertainty over the buyer's valuation and the seller's outside option. A long-lived seller makes offers to a long-lived buyer whose value is private information. There may exist a short-lived buyer whose value is higher than that of the long-lived buyer. The arrival of the short-lived buyer, if she exists, is determined by a Poisson process. We characterize the unique equilibrium. The equilibrium displays interesting price fluctuations: in some periods, the seller charges a high price unacceptable to the long-lived buyer, in the hope that the short-lived buyer will appear in that period; in the other periods, he offers a price attractive to some values of the long-lived buyer. The price dynamics result from the interaction between two learning processes: exogenous learning about the existence of short-lived buyers, and endogenous learning about the long-lived buyer's value.