Optimal Trade Mechanisms with Adverse Selection and Inferential Mistakes

We study an adverse selection environment, where a rational seller can trade a good of which she privately knows its value to a buyer, and there are gains from trade. The buyer’s types differ in their degree of inferential abilities: A rational type correctly infers the value of the good from the seller’s offer, whereas a naive type under-appreciates the correlation between the seller’s private information and offer. We characterize the optimal menu mechanism that maximizes the social surplus. Notably, no matter how severe the adverse selection is (in particular, even when no trade is the unique possible outcome if all agents are rational), all types of buyers trade in the optimal mecha- nism. The rational buyer’s trade occurs at the expense of the naive buyer’s losses. We also investigate a consumer-protection policy of limiting the losses and discuss its implications.