Selling an Item through Persuasion
Zhikang Fan, Weiran Shen
Abstract
A monopolistic seller aims to sell an indivisible item to multiple potential buyers. Each buyer's valuation depends on their private type and the item's quality. The seller can observe the quality but it is unknown to buyers. This quality information is valuable to buyers, so it is beneficial for the seller to strategically design experiments that reveal information about the quality before deciding to sell the item to whom and at what price. We study the problem of designing a revenue-maximizing mechanism that allows the seller to disclose information and sell the item. First, we recast the revelation principle to our setting, showing that the seller can focus on one-round mechanisms without loss of generality. We then formulate the mechanism design problem as an optimization problem and derive the optimal solution in closed form. The optimal mechanism includes a set of experiments and payment functions. After eliciting buyers' types, the optimal mechanism asks a buyer to buy and sets a price accordingly. The optimal information structure involves partitioning the quality space. Additionally, we show that our results can be extended to a broader class of distributions and valuation functions.