Reaping the Benefits of Bundling under High Production Costs

TL;DR

This paper introduces the PBDC mechanism, allowing customers to return goods for costs after bundling, which guarantees near-optimal profits under high production costs and improves upon previous bounds in revenue maximization.

Contribution

The paper proposes the PBDC mechanism with theoretical guarantees and demonstrates its superior performance over existing pricing schemes through simulations.

Findings

PBDC guarantees at least 1-6c^{2/3} of optimal profit under certain conditions.

Either PBDC or individual sales achieve at least 1/5.2 of the optimal profit.

PBDC outperforms other simple pricing schemes in simulations.

Abstract

It is well-known that selling different goods in a single bundle can significantly increase revenue. However, bundling is no longer profitable if the goods have high production costs. To overcome this challenge, we introduce a new mechanism, Pure Bundling with Disposal for Cost (PBDC), where after buying the bundle, the customer is allowed to return any subset of goods for their costs. We provide two types of guarantees on the profit of PBDC mechanisms relative to the optimum in the presence of production costs, under the assumption that customers have valuations which are additive over the items and drawn independently. We first provide a distribution-dependent guarantee which shows that PBDC earns at least 1-6c^{2/3} of the optimal profit, where c denotes the coefficient of variation of the welfare random variable. c approaches 0 if there are a large number of items whose individual valuations have bounded coefficients of variation, and our constants improve upon those from the classical result of Bakos and Brynjolfsson (1999) without costs. We then provide a distribution-free guarantee which shows that either PBDC or individual sales earns at least 1/5.2 times the optimal profit, generalizing and improving the constant of 1/6 from the celebrated result of Babaioff et al. (2014). Conversely, we also provide the best-known upper bound on the performance of any partitioning mechanism (which captures both individual sales and pure bundling), of 1/1.19 times the optimal profit, improving on the previously-known upper bound of 1/1.08. Finally, we conduct simulations under the same playing field as the extensive numerical study of Chu et al. (2011), which confirm that PBDC outperforms other simple pricing schemes overall.