Screening with Persuasion

TL;DR

This paper studies a nonlinear pricing model where sellers optimize both product screening and buyer persuasion, revealing that optimal mechanisms involve finite signals and pooling strategies to minimize informational rents.

Contribution

It proves that optimal mechanisms always have finitely many signals and items, and characterizes conditions for value pooling and single-item menus.

Findings

Optimal mechanisms have finitely many signals and items.

Value pooling is optimal when buyer value entropy exceeds a threshold.

Under certain conditions, the optimal menu offers only a single item.

Abstract

We analyze a nonlinear pricing model where the seller controls both product pricing (screening) and buyer information about their own values (persuasion). We prove that the optimal mechanism always consists of finitely many signals and items, even with a continuum of buyer values. The seller optimally pools buyer values and reduces product variety to minimize informational rents. We show that value pooling is optimal even for finite value distributions if their entropy exceeds a critical threshold. We also provide sufficient conditions under which the optimal menu restricts offering to a single item.