The value of an informed bidder in common value auctions

I compare two information structures in a common value first-price auction with two bidders: In one, each of the two bidders knows only his own signal about the value of the object, and in the other, one of the bidders learns his opponent's signal as well. Gaining the additional information in the second information structure makes the informed bidder worse off if the value is submodular in the bidders' signals and better off if it is supermodular. If the value is supermodular, then the seller's revenue tends to be lower with the informed bidder than without.     

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.     

Information acquisition in auctions: Sealed bids vs. open bids

This paper studies the incentives of a bidder to acquire information in an auction when her information acquisition decision is observed by the other bidders before bidding. Our results show that the sealed bid (second price) auction may induce more information acquisition about a common component of the value than the open (English) auction but less about the private component of the value. Moreover, we show that more information about the private value and less information about the common value may improve efficiency and revenue. Consequently, our results suggest new arguments in favor of the open auction.     

Equilibria in second price auctions with participation costs

We investigate equilibria of sealed-bid second price auctions with bidder participation costs in the independent private values environment. We focus on equilibria in cutoff strategies (participate and bid the valuation iff it is greater than the cutoff), since if a bidder finds it optimal to participate, she cannot do better than bidding her valuation. When bidders are symmetric, concavity (strict convexity) of the cumulative distribution function from which the valuations are drawn is a sufficient condition for uniqueness (multiplicity) within this class. We also study a special case with asymmetric bidders and show that concavity/convexity plays a similar role.     

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.     

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.     

Weak and strong multimarket bidding rings

We consider bidders who are simultaneously participating in private value second-price sealed bid auctions in multiple markets. While active in each market, each bidder is associated with a unique home market in which it can potentially serve as a ring center. Pairs of bidders can establish bilateral agreements to be members of bidding rings in each others’ home markets. Rings can be weak or strong depending respectively on whether side payments are permitted or not. Weak multimarket rings have been shown to take the form of exclusive groups of completely connected bidders. We consider strong multimarket bidding rings and show that they assume a radically different architecture of dominant groups, stars, and interlinked stars. Since bidding rings are tacit, and therefore unobservable, we develop observable implications of multimarket rings that can detect the existence of collusion as well as its form (i.e., weak or strong).     

An experimental investigation of the explosive effect in almost common value auctions

With only two bidders, a slight private value advantage in a common value auction is predicted to have an explosive effect on the allocation and revenue of the auction when using a second price and/or English clock mechanism. This paper uses the “wallet game” in an English clock mechanism with two players to test these predictions. The results show that the effect is proportional, not explosive, confirming the results of past experiments. A behavioral model with two types of players, naive and sophisticated, is developed and tested against the experimental data. In the model, naive players use a rule of thumb bidding function, while the sophisticated players are fully rational and, when forming their strategy (choosing the best response), correctly account for the probability that a rival is naive or sophisticated. We use cluster analysis to classify the players in the symmetric auctions as naive or sophisticated and a strict win/lose criteria to classify players in the asymmetric auctions. We find that those players classified as sophisticated are more aggressive in responding to high signals or advantaged status than their naive counterparts, but do not lower their bids relative to the naive players when receiving low signals or when regular.     

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.     

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.     

Monotonicity and Rationalizability in a Large First Price Auction

This paper proves that the monotonicity of bidding strategies together with the rationality of bidders implies that the winning bid in a first price auction converges to the competitive equilibrium price as the number of bidders increases ( Wilson, 1977 ). Instead of analysing the symmetric Nash equilibrium, we examine rationalizable strategies ( Bernheim (1984) , Pearce (1984) ) among the set of monotonic bidding strategies to prove that any monotonic rationalizable bidding strategy must be within a small neighbourhood of the „truthful” valuation of the object, conditioned on the signal received by the bidder. We obtain an information aggregation result similar to that of Wilson (1977) , while dispensing with almost all symmetric assumptions and using a milder solution concept than the Nash equilibrium. In particular, if every bidder is ex ante identical, then any rationalizable bidding strategy must be within a small neighbourhood of the symmetric Nash equilibrium. In a symmetric first price auction, the symmetry of outcomes is implied rather than assumed.     

Bidding behavior and experience in internet auctions

We study the role of experience in internet art auctions by analyzing repeated bidding by the same bidder in a unique longitudinal field dataset. Our results show that experience significantly lowers the level of bids suggesting that bidders change their bidding behavior throughout time. Participating in more than ten auctions brings down average bids by up to 26%. We further test several possible explanations for the observed learning behavior and show that the change in bidding strategy is a result of a change in within-auction behavior that is generated with experience. Our results are robust to concerns of endogenous participation as well as bidder fixed effects.     

Multi-unit auctions with private information: an indivisible unit continuous price model

We construct a model of multi-unit auctions in which I bidders bid for two indivisible units of a common value good. Using a first-order approach, we find that there are equilibria in which bidders bid the same price for both units in the discriminatory auction, but not in the uniform auction. When there are only two bidders, under certain conditions, there are linear equilibria for both the discriminatory and the uniform auction formats. In all equilibria, bidders equalize the expected marginal benefit of bidding to the marginal costs of bidding. We show that comparison of the seller??s expected revenue across auction formats depends only on the ratio of the precision of private information to the precision of public information.     

Collusive Bidding: Lessons from the FCC Spectrum Auctions

The Federal Communications Commission (FCC) spectrum auctions use a simultaneous ascending auction design. Bidders bid on numerous communication licenses simultaneously, with bidding remaining open on all licenses until no bidder is willing to bid higher on any license. With full revelation of bidding information, simultaneous open bidding allows bidders to send messages to their rivals, telling them on which licenses to bid and which to avoid. These strategies can help bidders coordinate a division of the licenses, and enforce the proposed division by directed punishments. We examine solutions to mitigate collusive bidding in the spectrum auctions, and then apply these ideas to the design of daily electricity auctions.     

On the effects of joint bidding in independent private value auctions: An experimental study

This article explores the effect of a subset of symmetric bidders joining to bid together. Possible applications include mergers, collusion and joint-bidding arrangements. The change produces a “strong” party with a more advantageous value distribution than the remaining “weak” bidder(s). The predicted effects include inefficiency, a decrease in the sellerʼs revenue, and higher biddersʼ payoffs. Under risk neutrality, the members of the strong party benefit less than the weak bidders. The prediction is reversed when the bidders are sufficiently risk-averse. These hypotheses are tested experimentally. Contrary to the theory, joint bidding increases efficiency and the sellerʼs revenue decreases by less than expected. Strong bidders benefit more than weak bidders indicating that incentives to bid jointly may be greater than hypothesized. Additionally, the experiment assesses the effect of group decision-making. A Nash equilibrium prediction for individual–group differences based on differences in risk attitudes is not supported by the data.     

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.     

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.     

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.     

Asymmetric information about rivals'' types in standard auctions

We study auctions in which bidders may know the types of some rival bidders but not others. This asymmetry in bidders' knowledge about rivals' types has different effects on the two standard auction formats. In a second-price auction, it is weakly dominant to bid one's valuation, so the knowledge of rivals' types has no effect, and the good is allocated efficiently. In a first-price auction, bidders refine their bidding strategies based on their knowledge of rivals' types, which yields an inefficient allocation. We show that the inefficient allocation in the first-price auction translates into a poor revenue performance. Given a standard regularity condition, the seller earns higher expected revenue from the second-price auction than from the first-price auction, whereas the bidders are better off from the latter.     

A Study of Collusion in First-Price Auctions

This paper examines the bidding for school milk contracts in Florida and Texas during the 1980s. In both states firms were convicted of bid-rigging. The data and legal evidence suggest that the cartels in the two states allocate contracts in different ways: One cartel divides the market among members, while the other cartel also uses side payments to compensate members for refraining from bidding. We show that both forms of cartel agreements are almost optimal, provided the number of contracts is sufficiently large.
In the auction the cartel bidder may face competition from non-cartel bidders. The presence of an optimal cartel induces an asymmetry in the auction. The selected cartel bidder is bidding as a representative of a group and has on average a lower cost than a non-cartel bidder. The data support the predicted equilibrium bidding behaviour in asymmetric auctions in accordance with optimal cartels.