Premium auctions and risk preferences: An experimental study

In premium auctions, the highest losing bidder receives a reward from the seller. This paper studies the private value English premium auction (EPA) for different risk attitudes of bidders. We explicitly derive the symmetric equilibrium for bidders with CARA utilities and conduct an experimental study to test the theoretical predictions. In our experiment, subjects are sorted into risk-averse and risk-loving groups. We find that revenues in the EPA are significantly higher when bidders are risk loving rather than risk averse. These results are partly consistent with theory and confirm the general view that bidders' risk preferences constitute an important factor that affects bidding behavior and consequently also the seller's expected revenue. However, individual subjects rarely follow the equilibrium strategy and revenue in our experiment is lower than in the symmetric equilibrium.     

Endogenous entry and self-selection in private value auctions: An experimental study

This paper presents the results of an experimental study of endogenous entry in first-price independent private value auctions. N potential bidders simultaneously decide whether to participate in an auction or receive a known outside option. In the second stage, entrants submit bids after learning their own private values and the number of entrants. An equilibrium model of heterogeneous risk averse bidders implies a self-selection effect, where bidding in the auction is lower with endogenous entry because only less risk averse bidders enter. This effect is confirmed by the experiment. We also observe excessive entry relative to the theoretical model.     

Auctioning Risky Conservation Contracts

Conservation auctions have the potential to increase the efficiency of payments to farmers to adopt conservation-friendly management practices by fostering competition among them. The literature considers bidders that have complete information about the costs of adoption and optimal bidding behavior reflects this information advantage. Farmers seek information rents and bids decrease when risk aversion increases because farmers are more averse to losing the auction. We contribute to the literature by allowing for cost risk. Our paper shows that farmers must balance the risk of losing the auction (thus foregoing information rent) with the risk of submitting a bid that is not high enough to pay the costs of adopting conservation practices (thus incurring losses). We design an experiment to trade off these two risks and examine how risk aversion affects bidding behavior when participants face different sources and levels of risk. Our experiment contributes to a small literature on experimental auctions with risky product valuations. We find that participants decrease their bids as risk aversion increases, even in auctions with cost risk, suggesting that the risk of losing the auction dominates. These findings uncover new challenges for the practical implementation of conservation auctions as an efficient policy instrument.     

REPUTATIONAL BIDDING

We consider auctions where bidders care about the reputational effects of their bidding and argue that the amount of information disclosed at the end of the auction will influence bidding. We focus on bid disclosure rules that capture all of the realistic cases. We show that bidders distort their bidding in a way that conforms to stylized facts about takeovers/licence auctions. We rank the disclosure rules in terms of their expected revenues and find that, under certain conditions, full disclosure will not be optimal. First‐price and second‐price auctions with price disclosure are not revenue equivalent and we rank them.     

An experiment on auctions with endogenous budget constraints

We perform laboratory experiments comparing auctions with endogenous budget constraints. A principal imposes a budget limit on a bidder (an agent) in response to a principal-agent problem. In contrast to the existing literature where budget constraints are exogenous, this theory predicts that tighter constraints will be imposed in first-price auctions than in second-price auctions, tending to offset any advantages attributable to the lower bidding strategy of the first-price auction. Our experimental findings support this theory: principals are found to set significantly lower budgets in first-price auctions. The result holds robustly, whether the principal chooses a budget for human bidders or computerized bidders. We further show that the empirical revenue difference between first- and second-price formats persists with and without budget constraints.     

Outside options: Another reason to choose the first-price auction

In this paper we study equilibrium and experimental bidding behaviour in first-price and second-price auctions with outside options.We find that bidders do respond to outside options and to variations of common knowledge about competitors’ outside options. However, overbidding in first-price auctions is significantly higher with outside options than without. First-price auctions yield more revenue than second-price auctions. This revenue-premium is significantly higher with outside options. In second-price auctions the introduction of outside options has only a small effect.     

eBay’s proxy bidding: A license to shill

We introduce a bidding strategy which allows the seller to extract the full surplus of the high bidder in eBay auctions. We call this a “Discover-and-Stop” bidding strategy and estimate that 1.39 percent of all bids in eBay auctions are placed by sellers (or accomplices) who execute this strategy. We argue that this kind of shill bidding is unnecessarily effective due to eBay’s proxy system and the predictability of other bidders’ bids. We also model eBay auctions with shill bidding and find that, in equilibrium, eBay’s profits are higher with shilling than without it. Finally, to determine whether bidders have an incentive to bid on their own items, we mimic the bidding behavior of shill bidders in actual eBay auctions and find some evidence of the strategy’s success.     

Auctions with endogenous participation and an uncertain number of bidders: experimental evidence

Attracting bidders to an auction is a key factor in determining revenue. We experimentally investigate entry and bidding behavior in first-price and English clock auctions to determine the revenue implications of entry. Potential bidders observe their value and then decide whether or not to incur a cost to enter. We also vary whether or not bidders are informed regarding the number of entrants prior to placing their bids. Revenue equivalence is predicted in all four environments. We find that, regardless of whether or not bidders are informed, first-price auctions generate more revenue than English clock auctions. Within a given auction format, the effect of informing bidders differs. In first-price auctions, revenue is higher when bidders are informed, while the opposite is true in English clock auctions. The optimal choice for an auction designer who wishes to maximize revenue is a first-price auction with uninformed bidders.     

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.     

Bidding in private-value auctions with uncertain values

Auctions are often used to sell idiosyncratic goods difficult for potential bidders to value ex ante. Laboratory auctions with uncertainty over final values in this experiment resulted in 18% and 27% of bids above the expected value of the item in private-value first-price and English auctions, respectively. Risk-seeking preferences as measured on an individual decision task cannot explain overbidding and the first-price auction results suggest that risk aversion may not be a good explanation for bidding behavior observed with certain values. Several candidate explanations fail to explain overbidding, rather it appears to stem from some bidders who are prone to overbidding. Relative to first-price auctions, the size and frequency of overbids are significantly larger in English auctions, while more English auctions are won by overbidders. Differences between the formats appear to be driven by the dynamic nature of English auctions which is consistent with popular notions of “auction fever.”     

A non-expected utility model and its application in practical auctions

ABSTRACT

This article presents a non-expected utility decision model which is nonlinear in the winning probabilities. The model not only explicitly expresses bidders’ attitudes to risk, but also addresses their preference over the bidding criteria. To demonstrate how to apply the model in the practical auction design, the first- and second-price auctions with both commission rate and reserve price are examined, respectively. For nonrisk-neutral bidders, the equilibrium bidding strategies are characterized, in which the commission rate has a significant influence on the bidding strategy through the critical valuation. However, the existence of the optimal commission rate is uncertain, but once it exists, it depends on the information rent of the highest or second highest order valuation in terms of the inverse hazard rate. With risk-aversion bidders, the only difference to the optimal reserve price is a constant between the first- and second-price auctions. The revenue comparisons show that the classical Revenue Equivalence Theorem fails in practical auctions with the commission rate. This article extends the application of the decision-making model in the auction design in theory and provides some guidance for the auction house and the seller to make their decisions in reality.     

DEMAND REDUCTION IN MULTI‐UNIT AUCTIONS WITH VARYING NUMBERS OF BIDDERS: THEORY AND EVIDENCE FROM A FIELD EXPERIMENT*

Recent auction theory and experimental results document strategic demand reduction by bidders in uniform‐price auctions. The present article extends this area of research to consider the effects of varying the number of bidders. Our theoretical model predicts that demand reduction should decrease with an increase in the number of bidders. Considerable demand reduction remains even in the asymptotic limit, although truthful bidding yields profits very close to those of equilibrium play. We experimentally confirm several of our predictions by examining bidding behavior of subjects in an actual marketplace, auctioning dozens of sportscards using both uniform‐price and Vickrey auction formats.     

Auctioning divisible goods

Summary. We derive equilibrium bidding strategies in divisible good auctions for asymmetrically informed risk neutral and risk averse bidders when there is random noncompetitive demand. The equilibrium bid schedules contain both strategic considerations and explicit allowances for the winner's curse. When the bidders' information is symmetric, the strategic aspects of bidding imply that there always exist equilibria of a uniform-price auction with lower expected revenue than provided by a discriminatory auction. When bidders are risk averse, there may exist equilibria of the uniform-price auction that provide higher expected revenue than a discriminatory auction. Received: November 4, 1999; revised version: March 9, 2001     

Expected revenue of all-pay auctions and first-price sealed-bid auctions with budget constraints

We show that all-pay auctions dominate first-price sealed-bid auctions when bidders face budget constraints. This ranking is explained by the fact that budget constraints bind less frequently in the all-pay auctions, which leads to more aggressive bidding in that format.     

Empirical Implications of Equilibrium Bidding in First-Price, Symmetric, Common Value Auctions

This paper studies federal auctions for wildcat leases on the Outer Continental Shelf from 1954 to 1970. These are leases where bidders privately acquire (at some cost) noisy, but equally informative, signals about the amount of oil and gas that may be present. We develop tests of rational and equilibrium bidding in a common values model that are implemented using data on bids and ex post values. We also use data on tract location and ex post values to test the comparative static prediction that bidders may bid less aggressively in common value auctions when they expect more competition. We find that bidders are aware of the "winner's curse" and their bidding is largely consistent with equilibrium.     

Late and multiple bidding in second price Internet auctions: Theory and evidence concerning different rules for ending an auction

In second price Internet auctions with a fixed end time, such as those on eBay, many bidders submit their bids in the closing minutes or seconds of an auction. We propose an internet auction model, in which very late bids have a positive probability of not being successfully submitted, and show that late bidding in a fixed deadline auction can occur at equilibrium in auctions both with private values and with uncertain, dependent values. Late bidding may also arise out of equilibrium, as a best reply to incremental bidding. However, the strategic advantages of late bidding are severely attenuated in auctions that apply an automatic extension rule such as auctions conducted on Amazon. Field data show that there is more late bidding on eBay than on Amazon, and this difference grows with experience. We also study the incidence of multiple bidding, and its relation to late bidding.     

Does asymmetric information affect the premium in mergers and acquisitions?

We test the influence of information asymmetry on the premium paid for an acquisition. We analyze mergers and acquisitions as English auctions. The theory of dynamic auctions with private and common value predicts that more informed bidders may pay a lower price. We test that prediction with a sample of 1,026 acquisitions in the United States between 1990 and 2007. We assume that blockholders of the target's shares are better informed than other bidders because they possess privileged information on the target. Our empirical results show that blockholders pay a much lower premium than do other buyers     

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 for the future: signaling in auctions with an aftermarket

This paper considers auctions where bidders compete for an advantage in future strategic interactions. When bidders wish to exaggerate their private information, equilibrium bidding functions are biased upwards as bidders attempt to signal via the winning bid. Signaling is most prominent in second-price auctions where equilibrium bids are “above value.” In English and first-price auctions, signaling is less extreme since the winner incurs the cost of her signaling choice. The opportunity to signal lowers bidders’ payoffs and raises revenue. When bidders understate their private information, separating equilibria need not exist and the auction may not be efficient.     

Industry concentration in common value auctions: theory and evidence

We examine theoretically and experimentally two countervailing effects of industry concentration in common value auctions. Greater concentration of information among fewer bidders reduces competition but increases the precision of private estimates. We demonstrate that this generally leads to more aggressive bidding. However, the reduction in competition dominates the informational effects, resulting in lower prices. We examine these hypothesized effects experimentally by conducting a series of auctions with constant informational content but distributed among a varying number of bidders. The experimental results are consistent with our theoretical predictions. The authors would like to thank Octavian Carare, Eric Friedman, Luke Froeb, Ron Harstad, Toshi Iizuka, Mike Rothkopf, Charles Thomas, and two anonymous referees, for many useful comments and suggestions.