Optimizing merchant revenue with rebates

We study an online advertising model in which the merchant reimburses a portion of the transacted amount to the customer in a form of rebate. The customer referral and the rebate transfer might be mediated by a search engine. We investigate how the merchants can set rebate rates across different products to maximize their revenue. We consider two widely used demand models in economics-linear and log-linear-and explain how the effects of rebates can be incorporated in these models. Treating the parameters estimated as inputs to a revenue maximization problem, we develop convex optimization formulations of the problem and combinatorial algorithms for solving them. We validate our modeling assumptions using real transaction data. We conduct an extensive simulation study to evaluate the performance of our approach on maximizing revenue, and found that it generates significantly higher revenues for merchants compared to other rebate strategies. The rebate rates selected are extremely close to the optimal rates selected in hindsight.