A Constructive Characterization of Optimal Bundling

TL;DR

This paper offers a constructive method to determine optimal bundling strategies for monopolists selling multiple goods, emphasizing deterministic menus and introducing the concept of tree bundling as an effective sales approach.

Contribution

It provides a sufficient condition linking the monopolist's problem to the upper envelope of marginal revenues, enabling a constructive algorithm for optimal menu design and characterizing tree bundling as optimal under certain conditions.

Findings

Optimal mechanism is deterministic and implementable via a menu of bundles.

A constructive algorithm for computing the optimal menu by eliminating dominated bundles.

Tree bundling is shown to be optimal under specific conditions, reflecting real-world sales practices.

Abstract

This paper studies a monopolist selling multiple goods to a consumer with one-dimensional private types. I provide a sufficient condition under which the monopolist's problem is equivalent to finding the upper envelope of the marginal revenue curves. This approach guarantees that the optimal mechanism is deterministic and can be implemented via a menu of bundles. I further characterize this upper envelope using a dominance notion. This characterization yields a constructive algorithm to compute the optimal menu by iteratively eliminating dominated bundles. As my main application, I use this framework to introduce and provide sufficient conditions for the optimality of tree bundling, a common but previously unmodeled sales strategy where the optimal menu contains a root bundle but features distinct upgrade paths. This structure captures prevalent sales practices across industries, from automobile manufacturers offering base models with customizable upgrade packages, to software companies allowing modular feature additions. This structure captures prevalent sales practices across industries, from automobile manufacturers offering base models with customizable upgrade packages, to software companies allowing modular feature additions.