Dynamic Bargaining in a Supply Chain with Asymmetric Demand Information

We analyze a dynamic bargaining game in which a seller and a buyer negotiate over quantity and payment to trade for a product. Both firms are impatient, and they make alternating offers until an agreement is reached. The buyer is privately informed about his type, which can be high or low: the high type's demand is stochastically larger than the low type's. In the dynamic negotiation process, the seller can screen, whereas the buyer can signal information through their offers, and the buyer has an endogenous and type-dependent reservation profit. With rational assumptions on the seller's belief structure, we characterize the perfect Bayesian equilibrium of the bargaining game. Interestingly, we find that both quantity distortion and information rent may be avoided depending on the firms' relative patience, and the seller may reach an agreement with either the high type or the low type first, or with both simultaneously. Furthermore, we explore our model to characterize the effect of demand forecasting accuracy on firm profitability. We find that improved demand forecast benefits the buyer but hurts the seller when the buyer's forecasting accuracy is low. However, once the buyer's forecasting accuracy exceeds a threshold, both firms will benefit from further improvement of the forecast. This observation makes an interesting contrast to previous findings based on the one-shot principal--agent model, in which improvement of forecasting accuracy mostly leads to a win--lose outcome for the two firms, and the buyer has an incentive to improve his forecasting accuracy only when it is extremely low. This paper was accepted by Yossi Aviv, operations management.