Agree Now or Later? Strategic Vertical Bargaining with Limited Capacity and Symmetric Information

In this paper we study dynamic strategic bargaining in business-to-business markets wherein a seller and a buyer possess symmetric information and negotiate over the price of a product for which the seller has a limited capacity. Motivated by the microprocessor market, our model offers an explanation for the occasional observations of delayed price agreement in this market, which cannot be explained by existing theories, and sheds light on how to make tactical decisions such as when to propose, reject, and accept counter-offers. In our model, the buyer can choose to wait if the seller rejects the counter-offer; as a countermeasure, the seller threatens to sell part of the limited capacity to other buyers who may possibly arrive later; the probability of the arrival of other buyers is updated while waiting. The subgame perfect equilibrium predicts that (1) it is credible for the buyer to wait when the gain from the trade is low and that (2) the seller should encourage the focal buyer to wait when selling to other buyers is more profitable. If prices are always settled without delay, the seller can lose more than 10% of its revenue according to our numerical study. We also investigate how to optimize the posted price given the anticipated equilibrium of bargaining and show that incorrect anticipations of the time of agreement lead to ineffective prices, which can be 8% lower than the optimal price. [