Multi-to -one dimensional and semi-discrete screening

TL;DR

This paper analyzes a monopolist's multi-dimensional consumer screening problem with a one-dimensional product space, establishing conditions for nested solutions and developing methods for both discrete and continuous product sets.

Contribution

It introduces general conditions for nested solutions in multi-dimensional screening and provides a unified method for solving the problem in both discrete and continuous cases.

Findings

Nestedness condition simplifies analysis

Method applicable to discrete and continuous product spaces

Uniqueness established for discrete case

Abstract

We study the monopolist's screening problem with a multi-dimensional distribution of consumers and a one-dimensional space of goods. We establish general conditions under which solutions satisfy a structural condition known as nestedness, which greatly simplifies their analysis and characterization. Under these assumptions, we go on to develop a general method to solve the problem, either in closed form or with relatively simple numerical computations, and illustrate it with examples. These results are established both when the monopolist has access to only a discrete subset of the one-dimensional space of products, as well as when the entire continuum is available. In the former case, we also establish a uniqueness result.