Information Design in Optimal Auctions

TL;DR

This paper analyzes how information can be optimally designed in auctions with multiple buyers, characterizing structures that maximize buyer surplus or minimize seller revenue, revealing differences from single-buyer cases and effects of increasing buyer numbers.

Contribution

It provides explicit solutions for optimal information structures in multi-buyer auctions and compares buyer-optimal and seller-worst designs, highlighting differences from single-buyer scenarios.

Findings

Symmetric buyer-optimal and seller-worst information structures differ with multiple buyers.

The good is always sold under seller-worst information but not under buyer-optimal information.

As the number of buyers increases, both structures converge to no disclosure.

Abstract

We study the information design problem in a single-unit auction setting. The information designer controls independent private signals according to which the buyers infer their binary private values. Assuming that the seller adopts the optimal auction due to Myerson (1981) in response, we characterize both the buyer-optimal information structure, which maximizes the buyers' surplus, and the sellerworst information structure, which minimizes the seller's revenue. We translate both information design problems into finite-dimensional, constrained optimization problems in which one can explicitly solve for the optimal information structures. In contrast to the case with one buyer (Roesler and Szentes, 2017), we show that with two or more buyers, the symmetric buyer-optimal information structure is different from the symmetric seller-worst information structure. The good is always sold under the seller-worst information structure but not under the buyer-optimal information structure. Nevertheless, as the number of buyers goes to infinity, both symmetric information structures converge to no disclosure. We also show that in an ex ante symmetric setting, an asymmetric information structure is never seller-worst but can generate a strictly higher surplus for the buyers than the symmetric buyer-optimal information structure.