Multidimensional Screening with Precise Seller Information

TL;DR

This paper demonstrates that with sufficiently precise buyer information, simple pure bundling mechanisms outperform separate sales and nearly match the optimal revenue, with convergence to the first-best as information precision increases.

Contribution

It shows that increased seller information about buyer valuations makes pure bundling nearly optimal, providing a convergence rate analysis to the first-best revenue.

Findings

Pure bundling outperforms separate sales with precise information.

Pure bundling converges to the first-best revenue at the same rate as optimal mechanisms.

Separate sales have a slower, suboptimal convergence rate.

Abstract

A multi-product monopolist faces a buyer who is privately informed about his valuations for the goods. As is well-known, optimal mechanisms are in general complicated, while simple mechanisms -- such as pure bundling or separate sales -- can be far from optimal and do not admit clear-cut comparisons. We show that this changes if the monopolist has sufficiently precise information about the buyer's valuations: Now, pure bundling always outperforms separate sales; moreover, there is a sense in which pure bundling performs essentially as well as the optimal mechanism. To formalize this, we characterize how fast the corresponding revenues converge to the first-best revenue as the monopolist's information grows precise: Pure bundling achieves the same convergence rate to the first-best as optimal mechanisms; in contrast, the convergence rate under separate sales is suboptimal.