Component Pricing with a Bundle Size Discount

Abstract

Firms selling multiple products usually adopt bundle pricing in their marketing strategy for the purpose of extracting large consumer surplus. In this paper, we propose and analyze a bundling mechanism, referred to as component pricing with a bundle size discount (CPBSD), which sells bundles for the summed prices of the included products (component pricing) minus a discount based on the number of products purchased (bundle size discount). CPBSD is conceptually simple and has been widely used in real-world business settings. Theoretically, we show that CPBSD subsumes several well-studied bundling mechanisms as special cases. Moreover, we find instances in which CPBSD can generate infinitely more profits than the best of other common mechanisms as the number of products increases. We further prove that, under a general condition, CPBSD attains the optimal profit asymptotically for a large number of products among all bundle pricing mechanisms. From a practical perspective, we formulate a mixed-integer linear program for the optimal pricing scheme of CPBSD,  and we also develop an approximation algorithm for efficiently solving CPBSD in large-scale problems. Through comprehensive numerical experiments, we show that CPBSD achieves  superior performance in contrast to other bundling mechanisms. In particular, compared to bundle size pricing whose outstanding empirical performance has been extensively tested in the literature, CPBSD performs especially well when products are heterogeneous and the production costs are high. Furthermore, the outstanding performance of CPBSD is most pronounced when the potential surplus provided by products are negatively correlated with the product valuations. We also show that our approximation algorithm may achieve a performance that is very close to the optimal CPBSD. Given the theoretical guarantee and the computational efficiency, CPBSD presents an appealing selling mechanism for retailers to improve their profitability.

Keywords: bundle pricing, mixed integer programming