A stackelberg differential game theoretic approach for analyzing coordination strategies in a supply chain with retailer’s premium store brand

The present study examines a supply chain consisting of a manufacturer and a retailer. The manufacturer produces a product with a national brand (NB) and the retailer selling both the NB product and his own premium store brand (PSB) product. The manufacturer competes with the retailer through improving the quality by using innovation over time. It is assumed that both advertising and enhanced quality play positive roles in customers’ loyalty over time for the NB product. We propose four scenarios, including: (1) Decentralized (D), (2) Centralized (C), (3) Coordination with a revenue-sharing contract (RSH), and (4) Coordination with a two-part tariff contract (TPT). A Stackelberg differential game model is developed, and parametric analyses and managerial insights are provided based on a numerical example. Our results show that: (1) Introducing a PSB product alongside selling the NB product is profitable for the retailer, (2) In Scenario D and RSH, the manufacturer tries to increase the quality gap with the PSB product through innovation, (3) Customers’ loyalty leads to higher prices, levels of innovation, quality, and advertising for the NB product, (4) The TPT contract can lead to perfect coordination and yield higher profits for the manufacturer and the retailer. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s10479-023-05372-9.