Rebate has long been a crucial tool that has attracted researchers from a diverse range of fields including marketing and supply chain management. When a manufacturer uses a retailer for reaching end customers, the rebate strategy undertakes an additional dimension. Here we show whether the two rebate strategies, manufacturer rebate and channel rebate, can be the optimal choice for the manufacturer and the retailer. And we aim at full coordination with rebate. Game theory is exploited to identify the equilibrium rebate decisions, which are fully characterized with two rebate strategies considering rebate sensitivity. Furthermore, we demonstrate how the decisions depend on parameters, such as market size, rebate redemption rate, and competition intensity in monopoly and duopoly supply chain systems. Our work also coordinates the supply chain with two coordination policies and examines if they can achieve full coordination. Counterintuitive findings suggest that the channel rebate with sensitivity and discrimination is not effective and the manufacturer rebate is the unique optimal option. Besides, the coordination can be realized with a centralized rebate in monopoly setting when the manufacturer forgoes her own interest. Then full coordination can be achieved in duopoly setting with a new coordination policy, rebate combination, given the redemption rate for the channel rebate is lower compared with the manufacturer rebate. Managerial insights are suggested that offering rebates with discrimination can have significant inventory and coordination policy implications and can lead to a double win under a well-controlled redemption rate.
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