Multi-to -one dimensional and semi-discrete screening
Optimization and Control
2025-10-30 v2 Theoretical Economics
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.
Cite
@article{arxiv.2506.21740,
title = {Multi-to -one dimensional and semi-discrete screening},
author = {Omar Abdul Halim and Brendan Pass},
journal= {arXiv preprint arXiv:2506.21740},
year = {2025}
}