Optimal pricing timing for an e-commerce platform selling a private label on its own marketplace

In this paper, we examine the optimal timing for an e-commerce platform, which produces and sells a private label on its own marketplace, to set the retail price, utilizing the timing game framework of noncooperative game theory. Conventionally, game-theoretic supply chain models describing such a platform assume that simultaneous price competition occurs at the level of the retail market, where the platform and a third-party supplier determine their retail prices at the same point of time. Consistent with this conventional assumption, we first show that under a wholesale contract (i.e., reselling mode), the platform's profit is unaffected by the timing of price setting; thus, the platform may decide and announce the retail price of its private label at any point of time, including making a simultaneous price decision with the supplier. Meanwhile, a more notable result from our model is that under an agency contract (i.e., marketplace mode), such simultaneous price competition between the platform and the supplier never occurs. This suggests that the conventional assumption of simultaneous retail price competition must be reconsidered. Our model yields the useful managerial decision guideline that a platform concluding an agency contract should set the retail price of its private label earlier than or simultaneously with, but not later than, setting the marketplace fee or commission rate charged to a supplier. The result also means that the platform must determine the retail price of the private label prior to the supplier determining the retail price of its product.