A theory of bargaining deadlock

I study a dynamic one-sided-offer bargaining model between a seller and a buyer under incomplete information. The seller knows the quality of his product, while the buyer does not. During bargaining, the seller may receive an outside option, the value of which depends on the quality of the product. If the outside option is sufficiently important, there is an equilibrium in which the buyer's belief about the product's quality stays constant and she continues to make the same randomized offer throughout the bargaining process. As a result, the equilibrium behavior produces an outcome path that resembles a bargaining deadlock and its resolution. The equilibrium outcome exhibits bargaining delay that does not vanish even with frequent offers, and the limiting delay may exist even without a static adverse selection problem. Under stronger parametric assumptions, the equilibrium with deadlock is the only one in which behavior is monotonic in the buyer's belief.