arXiv subjects

Zhikang Fan

Publications and source records attributed to Zhikang Fan.

4 recordsLinked to original sources

arXiv2024

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.

cs.GT↗

arXiv2024

Selling an Item through Persuasion

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.

cs.GT↗

arXiv2024

Revenue Maximization Mechanisms for an Uninformed Mediator with Communication Abilities

Consider a market where a seller owns an item for sale and a buyer wants to purchase it. Each player has private information, known as their type. It can be costly and difficult for the players to reach an agreement through direct communication. However, with a mediator as a trusted third party, both players can communicate privately with the mediator without worrying about leaking too much or too little information. The mediator can design and commit to a multi-round communication protocol for both players, in which they update their beliefs about the other player's type. The mediator cannot force the players to trade but can influence their behaviors by sending messages to them. We study the problem of designing revenue-maximizing mechanisms for the mediator. We show that the mediator can, without loss of generality, focus on a set of direct and incentive-compatible mechanisms. We then formulate this problem as a mathematical program and provide an optimal solution in closed form under a regularity condition. Our mechanism is simple and has a threshold structure. Additionally, we extend our results to general cases by utilizing a variant version of the ironing technique. In the end, we discuss some interesting properties revealed from the optimal mechanism, such as, in the optimal mechanism, the mediator may even lose money in some cases.

cs.GT↗

arXiv2024

Optimal Mediation Mechanism in Bilateral Trade

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.

cs.GT↗