Information Structures in Optimal Auctions

A seller wishes to sell an object to one of multiple bidders. The valuations of the bidders are privately known. We consider the joint design problem in which the seller can decide the accuracy by which bidders learn their valuation and to whom to sell at what price. We establish that optimal information structures in an optimal auction exhibit a number of properties: (i) information structures can be represented by monotone partitions, (ii) the cardinality of each partition is finite, (iii) the partitions are asymmetric across agents. These properties imply that the optimal selling strategy of a seller can be implemented by a sequence of exclusive take-it or leave-it offers.Optimal Auction, Private Values, Information Structures, Partitions

Information Structures in Optimal Auctions

A seller wishes to sell an object to one of multiple bidders. The valuations of the bidders are privately known. We consider the joint design problem in which the seller can decide the accuracy by which bidders learn their valuation and to whom to sell at what price. We establish that optimal information structures in an optimal auction exhibit a number of properties: (i) information structures can be represented by monotone partitions, (ii) the cardinality of each partition is finite, (iii) the partitions are asymmetric across agents. These properties imply that the optimal selling strategy of a seller can be implemented by a sequence of exclusive take-it or leave-it offers

Linkage principle, Multi-dimensional Signals and Blind Auctions

We compare the seller’s expected revenue in a second price sealed bid auction for a single object in which bidders receive multidimensional signals. Bidders’ valuations for the object depend on their signals and a signal observed privately by the seller. We show in various examples that the seller can be better off not revealing publicly his signal. Hence the linkage principle does not necessarily hold when bidders receive multidimensional signals.Auction Theory; Linkage Principle; Multidimensional Signals; Blind Auctions

Mechanism Design with Limited Information: The Case of Nonlinear Pricing

We analyze the canonical nonlinear pricing model with limited information. A seller offers a menu with a finite number of choices to a continuum of buyers with a continuum of possible valuations. By revealing an underlying connection to quantization theory, we derive the optimal finite menu for the socially efficient and the revenue-maximizing mechanism. In both cases, we provide an estimate of the loss resulting from the usage of a finite n-class menu. We show that the losses converge to zero at a rate proportional to 1/n^2 as n becomes large.Mechanism design, Limited information, Nonlinear pricing, Quantization, Lloyd-max optimality

Competition for Access and Full Revelation of Evidence

A decision maker must divide a prize between multiple agents. The prize may be divisible (e.g., a budget, pork-barrel spending) in which case he prefers to award larger shares of the prize to relatively more-qualified agents, or it may be non-divisible (e.g., jobs, college admissions) in which case he prefers to award the limited number of prizes to the most-qualified agents. He is, however, ex ante uncertain about agent qualications. Agents may directly reveal verifiable evidence about their qualifications to the decision maker only if the decision maker grants them \access" (e.g., he takes time to review their applications, hold interviews, or conduct an investigation). The time-constrained decision maker must decide which agents receive access, as he cannot grant access to everyone. One way to award access is through a competition, where agents submit payments (e.g., time, money) and higher payments correspond to a greater likelihood of receiving access. The analysis shows that there always exists competition for access mechanisms in which the decision maker becomes fully informed about the qualifications of all agents (even though only some agents reveal their qualifications through access). That is, the decision maker can award access in such a way that he always becomes fully informed and chooses his preferred prize allocation. The paper derives such full-revelation mechanisms, and determines when awarding access through a traditional all-pay auction is sufficient for full revelation.Verifiable evidence disclosure, hard information, all-pay auction, handicap auction, access, lobbying

Optimal Search Auctions

We study the design of profit maximizing single unit auctions under the assumption that the seller needs to incur costs to contact prospective bidders and inform them about the auction. With independent bidders’ types and possibly interdependent valuations, the seller’s problem can be reduced to a search problem in which the surplus is measured in terms of virtual utilities minus search costs. Compared to the socially efficient mechanism, the optimal mechanism features fewer participants, longer search conditional on the same set of participants, and inefficient sequence of entry.optimal auctions, search cost, search mechanism