Supplier encroachment under nonlinear pricing with imperfect substitutes: Bargaining power versus revenue-sharing

We explore the impact of nonlinear pricing (NP) on supplier encroachment in a supply chain, consisting of a retailer (he) and a supplier (she), who can sell through either the retailer, her direct channel, or both. The two channels' products are imperfect substitutes. The firms bilaterally negotiate over the wholesale price and the quantity using NP. To better align their behaviors, they can implement revenue-sharing (RS) to share the retailer's sales revenue. Our analysis shows that NP coupled with RS coordinates the supply chain under encroachment when the supplier seizes all the retailer's sales revenue. In what follows, the supplier subsidizes the retailer's acquisition of products through a negative wholesale price. Surprisingly, further increase of the supplier's direct selling cost and product substitution degree can benefit both firms. Contrary to the prior research, the retailer always hurts from the supplier's ability to encroach, even when an inactive direct channel is introduced. Furthermore, a supplier with weak power is more likely to benefit from encroachment, but one with strong power hurts from initiating an inactive direct channel when her retail disadvantage is limited. Our main results are robust even after altering some assumptions in the basic model.