Coarse Screening

TL;DR

The paper demonstrates that in buyer screening, the optimal coarse signal involves no more than three outcomes, with the bound determined by the effective policy dimension, influenced by limited liability and information costs.

Contribution

It establishes a universal bound on the complexity of optimal signals in screening, linking information design to rational inattention and extending to any convex information cost.

Findings

Optimal signals are no more than three outcomes regardless of type space.

Limited liability constrains the price and signal structure, leading to binary signals without investigation.

Universal function governs buyer participation under investigation, connecting information design to rational inattention.

Abstract

A seller investigates a buyer before setting prices, balancing the cost of acquiring information against the gain from tailoring the contract to the buyer's private type. The optimal signal is coarse: no matter how rich the type space, the seller never needs more than three outcomes per buyer. The bound equals the number of independent post-signal decisions plus one, a quantity we call the effective policy dimension. Screening involves two decisions, whether to allocate and what to charge, giving the ternary bound. Limited liability is the source: without it, the price is pinned by the envelope, only the allocation decision remains, and signals are binary as in monitoring. The Myerson exclusion rule is an artifact of not investigating. With investigation, every marginal buyer trades with positive probability, governed by a universal function that connects information design to rational inattention. The bound holds for any strictly convex information cost.