We study the problem of designing revenue-maximizing mechanisms for a selfish mediator who facilitates trade between a buyer and a seller. We consider a setting where the mediator does not have information advantage and the buyer's valuation is interdependent with the seller's private information. The mechanism may involve multi-round negotiations and flexible fee structures. We show that the mediator can restrict attention to a class of joint menu-selection mechanisms, where each mechanism can be represented as a two-dimensional menu. Each party privately selects an option from their own dimension and the two options together determine the menu entry. The mediator then recommends both parties whether to trade based on the jointly selected menu entry. We then establish an impossibility trilemma: no mechanism can simultaneously satisfy incentive compatibility, obedience, and informativeness. Motivated by this result, we characterize the optimal mechanisms under two relaxation conditions. First, when the seller's cost is constant, the optimal mechanism exhibits a threshold structure: trade occurs whenever the quality of the item exceeds a threshold that is decreasing in the buyer's type. Consequently, low-typed buyers receive more information, which in turn gives the mediator more power to charge from them. Second, when the mediator has veto power, the optimal mechanism also takes a threshold form, but in the opposite direction: trade occurs only if the quality falls below a threshold that is increasing in the buyer's type. As a result, items with lower qualities are more likely to be traded and the corresponding sellers benefit more, which discourages sellers of high qualities from participating and gives rise to a ``lemons market'' effect.

翻译：本文研究自私中介在促进买卖双方交易时的收益最大化机制设计问题。我们考虑中介不具备信息优势且买方估值与卖方私有信息相互依存的情境。该机制可包含多轮协商与灵活的费用结构。我们证明中介可聚焦于一类联合菜单选择机制，其中每个机制均可表示为二维菜单：各方从其对应维度私有地选择一个选项，两个选项共同确定菜单条目。随后中介根据联合选定的菜单条目向双方提供是否交易的建议。我们进而建立了不可能性三元悖论：任何机制都无法同时满足激励相容性、服从性与信息性。基于此结论，我们在两种松弛条件下刻画了最优机制的特征。首先，当卖方成本恒定时，最优机制呈现阈值结构：当商品质量超过随买方类型递减的阈值时交易发生。因此低类型买方获得更多信息，这使中介能向其收取更高费用。其次，当中介具有否决权时，最优机制同样呈现阈值形式，但方向相反：仅当商品质量低于随买方类型递增的阈值时交易发生。这导致低质量商品更易成交，相应卖方获益更多，从而抑制高质量卖方参与市场，引发"柠檬市场"效应。