Bargaining with binary private information

Abstract

This paper examines bargaining between a seller and a buyer with a binary private valuation. The seller offers a price to the buyer in each period. We explicitly construct the complete equilibrium set via an induction argument both for the finite and infinite horizon cases. When the horizon is finite and the probability of a high buyer valuation is large, the seller consistently charges a high price, resulting in trade bursts at the outset and deadline, with constant trade rates in between. We also show that the seller may be worse off when the low buyer's valuation increases and that the buyer may be better off when the seller has commitment than when not. We relate our results to previous findings on bargaining with two-sided offers.