A Bargaining Model for a First-Time Interaction Under Asymmetric Beliefs of Supply Reliability

We consider the case of a first-time interaction between a buyer and a supplier who is unreliable in delivery. The supplier declares her estimate of the ability to meet the order obligations, but the buyer may have a different estimate, which may be higher or lower than the supplier’s estimate. We derive the Nash bargaining solution and discuss the role of using a down-payment or nondelivery penalty in the contract. For the case of buyer overtrust, the down-payment contract maximizes channel profits when the supplier’s estimate is public information. If the supplier’s estimate is private information, a nonsymmetric contract is shown to be efficient and incentive compatible. For the case of buyer undertrust, the contract structure is quite different as both players choose not to include down-payments in the contract. When delivery estimates are public information, a nondelivery penalty contract is able to maximize channel profits if the buyer uses the supplier’s estimate in making the ordering decision. If estimates are private information, channel profits are maximized only if the true estimates of both players are not far part. We also discuss the effect of different risk profiles on the nature of the bargaining solution. In three extensions of the model, we consider the following variants of the basic problem. First, we analyze the effect of early versus late negotiation on the bargaining solution. Then, we study the case of endogenous supply reliability, and finally, for the case of repeated interactions, we discuss the impact of updating delivery estimates on the order quantity and negotiated prices of future orders.