Private value perturbations and informational advantage in common value auctions

We analyze the value of being better informed than one's rival in a two bidder, second price common value auction. Standard models of these auctions do not pin down relative bidding postures, but we show that by adding small amounts of private value information, a unique equilibrium can be restored. Additional common value information affects a bidder's payoff both directly, by increasing his information rent, and indirectly, by shifting the relative bidding posture of his opponent. Although the latter effect need not be positive, we establish broad conditions under which bidders with more information do better than their rivals. We turn to information acquisition and release and show that the desire to influence relative bidding postures can lead sellers to create new information rents (by releasing information privately to only one bidder) and bidders to forego information rents (instead choosing to gather information that a rival already has).     

Private information revelation in common-value auctions

When a seller has information that could help bidders to estimate asset value, a dictum of auction theory has been that all such information should be publicly announced to bidders. The possibility of privately revealing this information to one or more bidders is introduced. Seller in some circumstances may attain higher expected revenue through revealing his information privately. Examples show that the role of private revelation is more complex than simply generating bidder asymmetry.     

Bidding in a possibly common-value auction

We analyze a second-price auction with two bidders in which only one of the bidders is informed as to whether the object is valued commonly. We show that any equilibrium strategy of the bidder who is uninformed must be part of an equilibrium when both bidders instead know that the auction is not common value, regardless of the way in which the values are different. We derive sufficient conditions for equilibrium existence.     

Multidimensional private value auctions

We consider parametric examples of symmetric two-bidder private value auctions in which each bidder observes her own private valuation as well as noisy signals about her opponent's private valuation. We show that, in such environments, the revenue equivalence between the first and second price auctions (SPAs) breaks down and there is no definite revenue ranking; while the SPA is always efficient allocatively, the first price auction (FPA) may be inefficient; equilibria may fail to exist for the FPA. We also show that auction mechanisms provide different incentives for bidders to acquire costly information about opponents’ valuation.     

Almost common values auctions revisited

In almost common-value auctions one bidder (the advantaged bidder) has a valuation advantage over all other (regular) bidders. It is well known that in second-price auctions with two bidders, even a slight private-value advantage can have an explosive effect on auction outcomes as the advantaged bidder wins all the time and auction revenue is substantially lower than in a pure second-price common-value auction. We explore the robustness of these results to the addition of more regular bidders in second-price auctions, and the extent to which these results generalize to ascending-price English auctions in an effort to provide insight into when and why one ought to be concerned about such slight asymmetries.     

Procurement auctions with ex-ante endogenous bribery

Corruption is a prevalent phenomenon in various procurement auctions. This paper explores a pattern of bribery between an auctioneer and a favored bidder, and also investigates the regulation scheme of buyer. In the model, the favored bidder is allowed to submit two bids simultaneously with the advantageous one to be announced; auctioneer decides the share of the difference between two bids which is the bribe transfer. The analysis shows that, the favored bidder does not participate in the corruption if his cost exceeds a threshold; otherwise he submits two bids whose difference is decreasing in the share. The corruption benefits both the auctioneer and the favored bidder but harms other bidders. The bribery endogenously leads to allocation inefficiency with a probability decreasing in the bribe share. Specifically, with two uniformly distributed bidders, we examine how the auctioneer optimizes the bribe share and how the buyer regulates the corruption. We find that, by driving the auctioneer to charge a higher bribe share that is less attractive for the favored bidder, severer regulation tends to reduce the probability of corruption. A buyer who adopts extremely severe regulation can exclude the corruption and achieve maximum social welfare, while a buyer who aims to maximize his own profit should tolerate some degree of the corruption.     

Collusion in one-shot second-price auctions

Summary. Most of the literature on collusive behavior in auctions ignores two important issues that make collusion difficult to sustain at least in one-shot interactions: the detection of cheating and the verification of bids. Colluding bidders may deceive each other by using shill bidders. Also, if the identities of the bidders and their bids are not published then it would be difficult to verify the bid of a colluding bidder. This paper addresses these problems in one shot second price auctions where one bidder offers another bidder a side payment in exchange for not participating in the auction, while the number of other bidders is stochastic. In spite of the barriers to collusion mentioned above, a simple side payment mechanism which depends only on the auction price is introduced. It induces a successful collusion, eliminates the verification problem, provides no incentive for the use of shill bidders and guarantees that the proponent obtains ex-post non-negative payoff. The colluding bidders are ex-ante strictly better off compared with the competitive case, irrespective of their types.Received: 27 November 2002, Revised: 28 January 2005, JEL Classification Numbers: C72, D44, D82.Yair Tauman: Correspondence toWe would like to thank an anonymous referee for very valuable comments and suggestions that significantly improved the paper. We thank Shmuel Zamir for a helpful discussion.     

The value of information in oligopoly with demand uncertainty

This paper discusses the value of information in supermodular and submodular games, using a simple duopoly model where the level of demand is uncertain. It is shown that the value of information issuperadditive (resp.,subadditive) between players if the game issupermodular (resp.,submodular). For example, in a Bertrand (resp., Cournot) market with (possibly imperfect) substitute products, one firm's information acquisition increases (resp., decreases) the other firm's incentive to acquire the same information. Furthermore, when the game is either supermodular or submodular, the value of information is higher when the player isexpected to be informed according to the opponent's belief than when the player is expected to be uninformed; this result is reversed when the game has asymmetric modularity (i.e., one player's action is substitutional to the other's, and the latter's action is complemental to the former's). These qualitative observations have a potential to be applied to a larger class of games with uncertainty where payoffs are smooth (e.g., twice continuously differentiable) in actions and states.     

Optimal collusion-proof auctions

We study an optimal collusion-proof auction in an environment where subsets of bidders may collude not just on their bids but also on their participation. Despite their ability to collude on participation, informational asymmetry facing the potential colluders can be exploited significantly to weaken their collusive power. The second-best auction — i.e., the optimal auction in a collusion-free environment — can be made collusion-proof, if at least one bidder is not collusive, or there are multiple bidding cartels, or the second-best outcome involves a non-trivial probability of the object not being sold. Regardless, optimal collusion-proof auction prescribes non-trivial exclusion of collusive bidders, i.e., a refusal to sell to any collusive bidder with positive probability.     

The insider's curse

The paper shows that in an open-ascending bid auction with multi-dimensional uncertainty about private and common value components, private information about the common value has negative value for a bidder if there are sufficiently many bidders. We discuss the role of the visibility of bids and the multi-dimensionality of private information for this result.     

On the informational inefficiency of discriminatory price auctions

We analyze bidding behavior in large discriminatory-price auctions in a common value setting where the number of objects is a non-trivial proportion of the number of bidders. We show that the average price paid in the auction is biased downward from the expected value of the objects, even in the competitive limit. We show that conditional on a signal that falls below a threshold, a bidder bids no more than the expected value of an object conditional on the signal and winning; while conditional on any signal that lies above the threshold the bid is strictly lower than the expected value conditional on the signal and winning.     

Credit contracting and bidding under wealth constraints

Summary. We model credit contracting and bidding in a first-price sealed-bid auction when bidder valuation and wealth are private information. An efficient separating equilibrium exists only if the wealth levels of both bidder types are sufficiently different. If not, high-valuation bidders signal by borrowing more and using less of their wealth – this is inefficient as wealth is a cheaper source of funds. An increase in the amount of borrowing required to signal does not necessarily decrease seller expected revenue. In contrast to separating equilibria, high-valuation bidders adopt pure strategy bids in pooling equilibria. Conditions are identified under which the lower bound on winning bids is higher in pooling than separating equilibria. Received: January 22, 2001; revised version: August 28, 2001     

Non-bidding equilibrium in an ascending core-selecting auction

This paper investigates the perfect Bayesian equilibrium in an ascending-price core-selecting auction, which is recently used in some countries? spectrum license auctions. We suppose that there are two identical items, two small bidders, and one large bidder. The small bidders demand only one unit of the item, whereas the large bidder wants both units. Package bidding ensures that the large bidder faces no exposure problem and behaves truthfully. However, one of the small bidders stops bidding at the beginning in the equilibrium. Although small bidders generally face the free-rider problem and have incentives to underbid, once a bidder is the only small one remaining, he bids truthfully. Stopping early induces the remaining bidder to behave truthfully. Hence, each small bidder wants to be the first to stop bidding. The free-rider problem is considerably mitigated when there are many small bidders.     

A common value auction model with endogenous entry and information acquisition

Summary Much of the auction literature assumes both a fixed number of bidders and a fixed information setting. This sidesteps the important and often costly decisions a potential bidder must make prior to an auction: Should I enter and, if I do, what level of resources should I expend evaluating the good prior to bidding? We answer these questions for a stylized information model of a common value auction. The expected selling price is shown to be the expected value of the good minus the expected aggregate entry and information costs of the bidders. Thus, the seller indirectly pays for these costs to the bidders. There are auctions where the seller seemingly restricts the bidders' information expenditures. While this restriction does influence the entry decision, we demonstrate that the overall effect can be to improve the selling price. Finally, the probability of entry and the chosen accuracy of the information are never more in the second-price auction than in the first-price auction, and the seller prefers the second-price auction.We are grateful for the comments and suggestions of seminar participants at the University of British Columbia, Dartmouth College, the University of Wisconsin, Yale University, and the International Conference on Game Theory and Economics at SUNY Stony Brook.     

The value of information for auctioneers

An auctioneer wants to sell an indivisible object to one of multiple bidders, who have private information about their valuations of the object. A bidder's information structure determines the accuracy with which the bidder knows her private valuation. The main result of the paper is that the auctioneer's revenue is a convex function of bidders' information structures. One implication is that assigning asymmetric information structures instead of symmetric information structures to bidders is always revenue-enhancing. This paper generalizes a result of Bergemann and Pesendorfer [D. Bergemann, M. Pesendorfer, Information structures in optimal auctions, J. Econ. Theory 137 (2007) 580–609], who show that revenue-maximizing information structures are asymmetric.     

Learning to bid: The design of auctions under uncertainty and adaptation

We examine auction design in a context where symmetrically informed adaptive agents with common valuations learn to bid for a good. Despite the absence of private valuations, asymmetric information, or risk aversion, bidder strategies do not converge to the Bertrand–Nash equilibrium strategies even in the long run. Deviations from equilibrium strategies depend on uncertainty regarding the value of the good, auction structure, the agents? learning model, and the number of bidders. Although individual agents learn Nash bidding strategies in isolation, the learning of each agent, by flattening the best-reply correspondence of other agents, blocks common learning. These negative externalities are more severe in second-price auctions, auctions with many bidders, and auctions where the good has an uncertain value ex post.     

Bidding behavior in competing auctions: Evidence from eBay

Much of the existing auction literature treats auctions as running independently of one another, with each bidder choosing to participate in only one auction. However, in many online auctions, a number of substitutable goods are auctioned concurrently and bidders can bid on several auctions at the same time. Recent theoretical research shows how bidders can gain from the existence of competing auctions, the current paper providing the first empirical evidence in support of competing auctions theory using online auctions data from eBay. Our results indicate that a significant proportion of bidders do bid across competing auctions and that bidders tend to submit bids on auctions with the lowest standing bid, as the theory predicts. The paper also shows that winning bidders who cross-bid pay lower prices on average than winning bidders who do not.     

A Simple Model of Expert and Non-Expert Bidding in First-Price Auctions

This paper studies the equilibrium bidding behavior in a first-price sealed-bid auction when the number of informed bidders is not common knowledge. Both the independent private values and the common value cases are analyzed, under the assumption that a “neutral” signal exists. In equilibrium, experts and non-experts draw their bids from distinct supports: experts bid in the upper and lower tail of the bidding distribution and non-experts randomize their bids in between. For common values, it is shown that the seller's expected revenue always decreases with the probability of a bidder being informed when this probability is small. The opposite result is shown for the case of independent private values.Journal of Economic LiteratureClassification Numbers: D44, D82.     

Strategic ignorance in a second-price auction

Suppose that bidders may publicly choose not to learn their values prior to a second-price auction with costly bidding. All equilibria with truthful bidding exhibit bidder ignorance when the number of bidders is sufficiently small. Ignorance considerations also affect the optimal reserve price.     

The value of information in asymmetric all-pay auctions

This note analyzes a two-player all-pay auction with incomplete information. More precisely, one bidder is uncertain about the size of the initial advantage of his rival modeled as a head start in the auction.I derive the unique Bayesian Nash equilibrium outcome for a large class of cumulative distribution functions of the head start. The stronger player generates an informational rent if and only if his head start distribution is not stochastically dominated by a uniform distribution. I identify why my results for an uncertain head start differ qualitatively from uncertainty about a cost function or a valuation.