Manufacturer Rebate Competition in a Supply Chain with a Common Retailer

We consider manufacturer rebate competition in a supply chain with two competing manufacturers selling to a common retailer. We fully characterize the manufacturers' equilibrium rebate decisions and show how they depend on parameters such as the fixed cost of a rebate program, market size, the redemption rate of rebate, the proportion of rebate-sensitive consumers in the market and competition intensity. Interestingly, more intense competition induces a manufacturer to lower rebate value or stop offering rebate entirely. Without rebate, it is known that more intense competition hurts the manufacturers and benefits the retailer. With rebate, however, more intense competition could benefit the manufacturers and hurt the retailer. We find similar counterintuitive results when there is a change in some other parameters. We also consider the case when the retailer subsidizes the manufacturers sequentially to offer rebate programs. We fully characterize the retailer's optimal subsidy strategy, and show that subsidy always benefits the retailer but may benefit or hurt the manufacturers. When the retailer wants to induce both manufacturers to offer rebate, he always prefers to subsidize the manufacturer with a higher fixed cost first. Sometimes the other manufacturer will then voluntarily offer rebate even without subsidy.