Reaping the Benefits of Bundling under High Production Costs

It has long been known in the economics literature that selling different goods in a single bundle can significantly increase revenue, even when the valuations for the goods are independent. However, bundling is no longer profitable if the goods have high production costs. To overcome this issue, we introduce pure bundling with disposal for cost (PBDC), where after buying the bundle, we allow the customer to return any subset of items for their production cost. We demonstrate using classical examples that PBDC captures the concentration effects of bundling while allowing for the flexibility of individual sales, extracting all of the consumer welfare in situations where previous simple mechanisms could not. Furthermore, we prove a theoretical guarantee on the performance of PBDC that holds for arbitrary independent distributions, using techniques from the mechanism design literature. We transform the problem with costs to a problem with negative valuations, extend the mechanism design techniques to negative valuations, and use the Core-Tail decomposition of Babaioff et al. from [BILW14] to show that either PBDC or individual sales will obtain at least 1 5.2 of the optimal profit. This also improves the bound of 16 from [BILW14]. We advance the upper bound as well, constructing two IID items with zero cost where pure bundling and individual sales can only earn 3+ln 2 3+2 ln 2 ≈ 1 1.188 as much revenue as mixed bundling. Our numerical experiments show that PBDC outperforms all other simple pricing schemes, including the bundle-size pricing (BSP) introduced by Chu et al. in [CLS08], under the same families of distributions used in [CLS08]. We also provide the first theoretical explanation for some of the great experimental successes in [CLS08]. All in all, our work establishes PBDC as a robust, computationally-minimal heuristic that is easy to market to consumers. ∗Operations Research Center, Massachusetts Institute of Technology, [email protected]. †Institute for Data, Systems, and Society, Department of Civil and Environmental Engineering, and Operations Research Center, Massachusetts Institute of Technology, [email protected]. 1 ar X iv :1 51 2. 02 30 0v 2 [ cs .G T ] 1 5 Ja n 20 16