Note. Optimal Promotion Strategies: A Demand-Sided Characterization

We generalize Narasimhan's (Narasimhan, Chakravarthi. 1988. Competitive promotional strategies. J. Bus. 61(4) 427--449.) model of retail promotion to include multiple products and general demand functions. Doing so allows us to further characterize optimal promotion strategies. We find that firms prefer to offer deeper promotions on products for which switching customers have stronger demand than loyal customers and/or for which the price sensitivity of demand is high for both switching and loyal customers. We further show that firms will offer deeper promotions on products which enjoy complementary relationships with other products that they sell rather than on products for which the firm sells a substitute.