Delivery arrangement in online distribution channels under different power structures

Logistics delivery is a critical but costly operation in e-commerce. The e-retailer who sells products online may ask the supplier to ship products to customers, and the supplier responds by accepting or rejecting such a delivery proposal. Motivated by these observations, we consider an online distribution channel with two competing suppliers and one common e-retailer and analytically characterize the equilibrium delivery arrangement based on the nonlinear delivery cost in the E-retailer-Stackelberg, Supplier-Stackelberg, and Vertical-Nash games. Our analysis reveals that the market follower might be more willing to deliver products than the market leader in each Stackelberg game. Counterintuitively, the e-retailer prefers undertaking the delivery when there is a large delivery diseconomy under each power structure but prefers asking both suppliers to deliver products when there is a delivery economy (a small delivery diseconomy) in the E-retailer-Stackelberg and Vertical-Nash games (Supplier-Stackelberg game). The suppliers agree to ship products only when the delivery economy is apparent in the E-retailer-Stackelberg game but reject to do so in the Vertical-Nash game; in the Supplier-Stackelberg game, they accept the delivery proposal even though there is a significant delivery diseconomy. Although both suppliers can benefit from refusing to undertake the delivery when there is fierce competition in each Stackelberg game, interestingly, they still agree to do so and trap themselves in a prisoner's dilemma. In each Stackelberg game, only shifting the delivery responsibility to the suppliers might achieve a triple-win situation for the channel members, consumers, and society; in the Vertical-Nash game, however, this situation never occurs, and the consumer surplus and social welfare are invariant to the delivery arrangement.