Optimal auctions under collusion of buyers with discrete valuations

The potential seller of an indivisible good faces two potential buyers whose valuations for the good are private information. We derive the optimal selling mechanism under the assumption that the buyers collude both when the valuations are independently distributed and when they are correlated. We find that when the valuations are independent the seller can obtain the same expected revenue as if the buyers behaved noncooperatively; if instend the valuations are correlated then collusion harms the seller. In this latter case, moreover, each buyer’s information at the collusion stage about the other buyer’s valuation turns out to be very relevant for the effectiveness of collusion.     

Advertising a second-price auction

This study examines a symmetric private-value second-price auction model in which the seller solicits bidders at a cost, sets a reserve price, and receives a payoff which is a convex combination of revenue and welfare. The bidder’s valuations are drawn from a distribution with a decreasing hazard rate and non-decreasing virtual valuations. We find that at equilibrium the seller adopts an advertising policy which minimizes the uncertainty over the number of participants, and sets a reserve price which only depends on the distribution of valuations and the weight on revenue in the objective function. A welfare-maximizing seller is shown to advertise more than a revenue-maximizing seller, and a ceteris paribus increase in the advertising level is proved to increase the expected winner’s rent.     

First-price auctions where one of the bidders’ valuations is common knowledge

We analyze a private and independent valuation first-price auction under the assumption that one of the bidders’ valuations is common knowledge. We show that no pure strategy equilibrium exists and we characterize a mixed strategy equilibrium in which the bidder whose valuation is common knowledge randomizes her bid while the other bidders play pure strategies. In an example with the uniform distribution, we compare the expected profits of seller and buyers in this auction with those in a standard symmetric private valuation model.     

The public release of information in first-price sealed-bid auctions

We determine the conditions under which the seller in a first-price sealed-bid auction has an incentive to reveal his private information about the mean of bidders’ valuations in order to increase his expected revenue. With risk-neutral bidders, we show that the seller’s expected revenue is higher when information is revealed. However, when bidders are risk-averse, this result does not necessarily hold; it depends on the bidders’ risk-aversion level and on the number of bidders.     

Optimal allocation mechanisms with single-dimensional private information

We study revenue-maximizing allocation mechanisms for multiple heterogeneous objects when buyers care about the entire allocation, and not just about the ones they obtain. Buyers’ payoff depends on their cost parameter and, possibly, on their competitors’ costs. Costs are independently distributed across buyers, and both the buyers and the seller are risk-neutral. The formulation allows for complements, substitutes and externalities. We identify a number of novel characteristics of revenue-maximizing mechanisms: First, we find that revenue-maximizing reserve prices depend on the bids of other buyers. Second, we find that when non-participation payoffs are type-dependent, revenue-maximizing auctions may sell too often, or they may even be ex-post efficient.     

Optimal two-object auctions with synergies

We design the revenue-maximizing auction for two objects when each buyer has bi-dimensional private information and a superadditive utility function (i.e., a synergy is generated if a buyer wins both goods). In this setting the seller is likely to allocate the objects inefficiently with respect to an environment with no synergies (see Armstrong, RES (2000)). In particular, the objects may be bundled too rarely or a buyer may win the bundle even though her valuations for the goods are weakly dominated by the values of another buyer.Received: 29 October 2001, Accepted: 29 October 2002, JEL Classification: D44, D82This paper has been written while the author was a member of the Dipartimento di Statistica e Matematica Applicata alle Scienze Umane "Diego De Castro", Universitá degli Studi di Torino, Italy. Valuable comments and suggestions were provided by Antonio Cabrales, Massimo Marinacci, three anonymous referees and, especially, by Mark Armstrong. The usual disclaimer applies.     

Optimal auctions and information disclosure

We characterise properties of optimal auctions if the seller may disclose information about the quality of the object for sale. We show that the seller maximizes his expected revenue by revelation of all information to all bidders and implementing a second price auction with appropriate reservation price.     

Must Sell

Why are moving sales a successful and widespread phenomenon? How can it be optimal for a seller to disclose her low valuation for the item to be sold? We propose an explanation based on the “lemons problem” in bargaining with asymmetric information about quality. Disclosing a low valuation signals that there are significant gains from trade, so that trade takes place when it wouldn't otherwise, and all agents are made better off.     

Information concentration in common value environments

We consider how information concentration affects a seller’s revenue in common value auctions. The common value is a function of $n$ random variables partitioned among $m \le n$ bidders. For each partition, the seller devises an optimal mechanism. We show that whenever the value function allows scalar sufficient statistics for each player’s signals, the mechanism design problem is well-defined. Additionally, whenever a common regularity condition is satisfied, a coarser partition always reduces revenues. In particular, any merger or collusion among bidders reduces revenue.     

Implementation of the revenue-maximizing auction by an ignorant seller

In a general auction framework with independent private values, we propose a game, with a simple economic interpretation, that allows to implement the revenue-maximizing auction outcome when the seller ignores the distributions of the different bidders’ valuations. In this detail-free implementation procedure, an ascending-price contest is organized and the winner volunteers a payment to the seller; this payment can then be challenged by another bidder who knows the distribution of the winner’s valuation.Received: 4 June 2003, Accepted: 4 April 2005, We have benefited from comments by seminar participants at the Econometric Society North American Winter Meeting and European Meeting, PURC University of Florida, University of Wisconsin, as well as by two referees and an Associate Editor. The authors also wish to acknowledge the hospitality of IDEI in Toulouse where they started this research. The second author acknowledges the financial support of CRSHC, CIRANO and the Bell University Labs.     

Determinants of Voluntary Disclosure of Sales in Small Private Companies in Belgium

Small businesses are the backbone of the economy in many countries. In Europe, for example, small companies represent more than 90 per cent of all companies (e.g., Lukacs, 2005 ). Although these companies represent such an important portion of the economy, few studies have examined their voluntary disclosure decisions. Because small companies have certain unique characteristics compared with their larger counterparts, the general applicability of past voluntary disclosure studies to small companies is questionable. Drawing on agency and proprietary cost theory, this study investigates whether ownership, competition, and accountant factors influence the decision to disclose financially sensitive information on a voluntary basis. Our results (using an e‐mail questionnaire to small private companies in Belgium, n = 1,068) indicate that nearly 40 per cent of the responding companies are not aware of their disclosure behavior. For companies that are aware of their disclosure behavior, the logistic regression analysis demonstrates that factors relating to the separation of ownership and control, namely the type of ownership and number of shareholders, are among the most important determinants in the voluntary disclosure decision of small private companies. Companies with at least one legal entity as an owner of a company are less likely to disclose, while companies with more shareholders are more likely to disclose. We also provide evidence that perceived competition and the default setting of the accounting software used have a significant influence on the voluntary disclosure behavior.     

Contract Renegotiation with Time-Varying Valuations

The paper characterizes optimal renegotiation-proof rental contracts in a model with adverse selection and hidden information. It generalizes the work of Hart and Tirole (1988) to the case of time-varying valuations. The paper considers a durable-goods monopolist who serves a nonanonymous buyer with time-varying valuation for the seller's good. The buyer's valuation has a persistent and a transient component; both are private information. The paper shows that for some range of prior beliefs the seller strictly prefers leasing to selling.     

He who must not be named

Landsberger et al. have studied a sealed bid first price auction with two players in which the ranking of the valuations is known. They argue that such a situation can arise in a sequential auction where only the name of the winner is revealed. In this paper we consider sequential auctions where two identical goods are sold sequentially to N players who are interested in both objects. In sealed bid auctions, no information is a priori revealed by the mechanism, but the seller can in principle reveal whatever he wants. We restrict our attention to the case where only the name of the winner is revealed to be in the context of Landsberger et al. for the second auction. The aim of the paper is to compare such a sequential auction with a simultaneous auction where both goods are sold as a bundle or equivalently with a sequential auction where no information is revealed. We first show that there exists an equilibrium of the sequential game in pure and monotone strategies. Then, the comparison of the seller's expected revenue in the two cases allows us to conclude that contrary to Landsberger et al.'s predictions, the seller can not use the information to increase his revenue. This result is obtained using simulations for a large class of distribution functions. The seller must not reveal the name of the winner between the two auctions and instead sell both goods using a simultaneous auction.Received: 31 July 2001, Accepted: 5 February 2003, JEL Classification: B44I wish to thank Laurent Linnemer, Thomas Ricke, Michael Visser and Shmuel Zamir for helpful comments and suggestions. I am very grateful to the referees and the associated editors in charge of my paper.     

Voluntary Disclosure and Analyst Forecast

Empiricists document that firms more often voluntarily disclose bad news than good news and link this pessimism to managers’ increased incentives not to fall short of earnings expectations. This paper analyzes the voluntary disclosure of a manager’s private information by explicitly considering her incentives to meet or beat an analyst’s earnings forecast. The model predicts that managers who face strong incentives to meet or beat these forecasts more frequently disclose bad news than good news in order to guide analysts’ expectations about future earnings downward. This pessimism is higher in markets with less informed managers and may hold even if the manager has strong incentives for high stock prices and meet-or-beat incentives are comparably low.     

A two-dimensional problem of revenue maximization

We consider the problem of finding the mechanism that maximizes the revenue of a seller of multiple objects. This problem turns out to be significantly more complex than the case where there is only a single object (which was solved by Myerson, 1981). The analysis is difficult even in the simplest case studied here, where there are two exclusive objects and a single buyer, with valuations uniformly distributed on triangular domains. We show that the optimal mechanisms are piecewise linear with either 2 or 3 pieces, and obtain explicit formulas for most cases of interest.     

Information Revelation in Procurement Auctions with Two‐Sided Asymmetric Information

A buyer needs to procure a good from one of two suppliers offering differentiated products and with privately observed costs. The buyer privately observes the own valuations for the products and (ex ante) decides how much of this information should be revealed to suppliers before they play a first score auction. Our main result is that the more significant is each supplier's private information on the own cost, the less information the buyer should reveal. We also examine the buyer's incentives to make untruthful announces.     

Information provision and consumer search behavior for products with asymmetric uncertainty

When selling multiple products with asymmetric uncertainty, should the seller disclose product information so that customers do not have to incur any cost to resolve their uncertainties; if so, which product should the seller choose? To address these questions, we consider a monopolist selling two substitutable products to a group of consumers. Each consumer has asymmetric uncertainty regarding the two products. A total of four different information provision structures are considered based on whether the seller discloses information about each product with the aim of determining which strategy provides the seller with the greatest revenue. We derive several interesting results. First, the optimal information provision strategy depends on the magnitude of uncertainty in relation to the product with lower uncertainty. Specifically, if the uncertainty regarding the product with lower uncertainty is sufficiently small, it is optimal for the seller to provide information about the product with higher uncertainty, otherwise, the seller should provide information about both products. Second, when only one product's information should be revealed, it is optimal for the seller to choose the product with higher uncertainty and charge a higher price. Third, withholding information on both products is never optimal for the seller. Finally, our main model is extended by examining the Mean-Preserving Spread setting, and the robustness of our main results is confirmed. Furthermore, we examine the situation in which a monopolist sells a single product with two main attributes. We find that each of the four information provision strategies can be optimal under various scenarios.     

Optimal auctions for asymmetrically budget constrained bidders

We consider an environment with a single divisible good and two bidders. The valuations of the bidders are private information but one bidder has a commonly known budget constraint. For this environment we derive the revenue maximizing subsidy free dominant strategy incentive compatible auction.      

Potential competition and quality disclosure

This study presents a model of quality disclosure in which an incumbent, through its quality and disclosure choices, influences the potential that a new entrant enters the market. In this regard, we consider a sequential framework in which the incumbent chooses its quality and decides whether to disclose it to the market; subsequently, the entrant makes the same decisions, if it enters the market. We show that the potential competition can create strategic incentives for the incumbent to choose nondisclosure, because the availability of information about the incumbent's quality promotes entry by enhancing the entrant's expected profit from the market. In addition, an analysis of the effects of mandatory disclosure laws suggests that they can be effective in encouraging new market entrants and in improving the product quality of established firms.     

食品安全信息披露的博弈分析

食品质量安全信息披露不足,导致消费者难以分辨食品的安全性,不能对市场中的食品产生信任。本文建立消费者与生产者的信号博弈模型并找寻了动态均衡路径,分析认为:食品生产企业要获得消费者信任并实现与低质量企业完全分离,必须披露更多的质量安全信息,同时高质量企业披露安全信息对企业有利。通过比较国外为获得消费者信任而加强食品安全信息披露的情况,指出现阶段国内食品安全信息披露的不足,提出引导高质量企业进行更多信息披露、加强信息沟通交流和落实信息披露机制的建议。