Coarse Screening
TLDR
This paper shows that sellers investigating buyers before pricing need only three signal outcomes per buyer, even with rich type spaces, due to limited liability.
Key contributions
- Optimal signals for sellers investigating buyers are coarse, requiring at most three outcomes per buyer.
- This ternary bound arises from the two decisions involved in screening: allocation and pricing.
- Limited liability is essential for the three-outcome bound; without it, signals become binary.
- Investigating buyers eliminates the Myerson exclusion rule, ensuring all marginal buyers trade.
Why it matters
This paper redefines optimal information acquisition for sellers, demonstrating that coarse signals are sufficient even with rich buyer types. It challenges the Myerson exclusion rule, ensuring marginal buyers trade, and links information design to rational inattention. This has significant implications for contract theory and market design.
Original 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.
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