Multi-Dimensional Screening with Endogenous Information Disclosure
Yang Cai, Yingkai Li, Jinzhao Wu
TL;DR
The paper investigates joint design of pricing and information disclosure for selling multiple heterogeneous products to a single, unit-demand buyer with potentially correlated valuations. By allowing the seller to choose the information structure, it shows that simple pricing mechanisms—especially uniform pricing with coarse horizontal disclosure—achieve a constant-factor approximation to the optimal revenue, with Rev ≥ $\tfrac{1}{2}$ OPT-Rev in general and improvements when pricing across products is allowed. It provides conditions under which full surplus extraction is possible (e.g., negative affiliation or exchangeability) and tight examples illustrating the limits of uniform pricing. The results highlight the practical impact of information design in multi-dimensional screening, suggesting that endogenous information can render simple mechanisms nearly optimal in settings where exogenous information would erode revenue. The work opens avenues for precise characterizations of the approximation ratio in larger $m$ and for extending these insights to broader valuation frameworks.
Abstract
We study multi-product monopoly pricing where the seller jointly designs the selling mechanism and the information structure for the buyer to learn his values. Unlike the case with exogenous information, we show that when the seller controls information, even uniform pricing guarantees at least half of the optimal revenue. Moreover, for negatively affiliated or exchangeable value distributions, deterministic pricing is revenue-optimal. Our results highlight the power of information design in making pricing mechanisms approximately optimal in multi-dimensional settings.