Optimal Fixed-Price Mechanism with Signaling

Consider a trade market with one seller and multiple buyers. The seller aims to sell an indivisible item and maximize their revenue. This paper focuses on a simple and popular mechanism--the fixed-price mechanism. Unlike the standard setting, we assume there is information asymmetry between buyers and the seller. Specifically, we allow the seller to design information before setting the fixed price, which implies that we study the mechanism design problem in a broader space. We call this mechanism space the fixed-price signaling mechanism. We assume that buyers' valuation of the item depends on the quality of the item. The seller can privately observe the item's quality, whereas buyers only see its distribution. In this case, the seller can influence buyers' valuations by strategically disclosing information about the item's quality, thereby adjusting the fixed price. We consider two types of buyers with different levels of rationality: ex-post individual rational (IR) and ex-interim individual rational. We show that when the market has only one buyer, the optimal revenue generated by the fixed-price signaling mechanism is identical to that of the fixed-price mechanism, regardless of the level of rationality. Furthermore, when there are multiple buyers in the market and all of them are ex-post IR, we show that there is no fixed-price mechanism that is obedient for all buyers. However, if all buyers are ex-interim IR, we show that the optimal fixed-price signaling mechanism will generate more revenue for the seller than the fixed-price mechanism.