We study information disclosure in competitive markets with adverse selection. Sellers privately observe product quality, with higher quality entailing higher production costs, while buyers trade at the market-clearing price after observing a public signal. Because sellers' participation in trade conveys information about quality, the designer faces endogenous constraints in the set of posteriors that she can induce. We reformulate the designer's problem as a martingale optimal transport exercise with an additional condition that rules out further information transmission through sellers' participation decisions, and characterize the optimal signals. When the designer maximizes trade volume, the solution features negative-assortative matching of inefficient and efficient sellers. When the objective is a weighted combination of price and surplus, optimal signals preserve this structure as long as the weight on the price is high enough, otherwise they fully reveal low-quality types while pooling middle types with high-quality sellers.
Paolo et al. (2025) studied this question.