Common Value Auctions Research Articles

Industry concentration in common value auctions: theory and evidence

Industry concentration in common value auctions: theory and evidence

Repeated common value auctions with asymmetric bidders

This paper considers a first price common value auction with one-sided private information among bidders. An object is rented each period to the highest bidder without revealing the bids made in previous periods. The paper extends single crossing arguments used in static games to show the existence of equilibrium in this repeated auction. The model predicts that bidders bid more aggressively in a repeated auction than in a static auction, because a higher bid increases the amount of information learned through bidding. The aggressive bidding behavior also implies that the per period revenue of the repeated auction is higher than that of the one-period counterpart. This bidding behavior leads to a theoretical explanation for the winner's curse in repeated auctions. In addition, the model yields predictions like an increasing wage schedule over time and the institution of a signing bonus that are consistent with labor market observations.

Compensating for the winner's curse: Experimental evidence

We conduct experiments on common value auctions with rationing. In each auction, the good is randomly allocated to one of the k highest bidders, at the ( k + 1 ) st highest price. When k > 1 , bidders are rationed. As the degree of rationing increases, the equilibrium bid function increases. Consistent with prior literature, we find that bidders suffer from the winner's curse and lose money on average. However, bids in the experiments do adjust in the appropriate direction as the degree of rationing changes, providing support for the comparative statics implications of the theory. Our results are consistent with subjects having an intuitive understanding of the winner's curse, but being unable to compute the equilibrium bid levels.

Learning Differences in Mixed Common Value Auctions

I examine the behavior of subjects in common value auctions with both experienced and inexperienced bidders in the same market. Subjects know that they are competing against both experienced and inexperienced subjects and can observe bidding behavior of their opponents after an auction round. The existence and common knowledge of mixed experience levels in the same auction market affects the bidding behavior of inexperienced bidders, and gender plays an important role: Inexperienced males bid more aggressively in auction market with mixed bidders compared to markets with only inexperienced bidders, but inexperienced females bid less aggressively. The mixed markets only have an effect on inexperienced bidders. Experienced bidders (males and females) do not react significantly different in mixed auction markets than in markets with only experienced bidders.

Why Do IPO Auctions Fail?

We document a somewhat surprising regularity: of the many countries that have used IPO auctions, virtually all have abandoned them. The common explanations given for the lack of popularity of the auction method in the US, viz., issuer reluctance to try a new experimental method, and underwriter pressure towards methods that lead to higher fees, do not fit the evidence. We examine why auctions have failed and verify, to the extent possible, that they are consistent with what academic theory predicts. Both uniform price and discriminatory auctions are plagued by unexpectedly large fluctuations in the number of participants. The free rider problem and the winner's curse hamper price discovery and discourage investors from participating in auctions. Calculating the optimal bids in large multi-unit common value auctions with endogenous entry imposes a huge computational burden. With IPOs taking place sporadically, and each firm being different, auctions are likely to end up being unstable.

Affiliated Common Value Auctions with Differential Information: The Two Bidder Case

I study affiliated, pure common-value auctions with ex-ante asymmetric buyers. For the two-buyer case I characterize and prove uniqueness of the equilibrium of hybrid auctions where the payment is a weighted average of the highest and second-highest bids. A recursive method to explicitly compute the equilibrium is presented. It is shown that any hybrid auction yields at least as much revenue as the first-price auction. In particular, the equilibrium of the second-price auction, obtained in the limit by letting the weight of the highest bid go to zero, revenue-dominates the first-price auction.

Barking up the right tree: Are small groups rational agents?

Both mainstream economics and its critics have focused on models of individual rational agents even though most important decisions are made by small groups. Little systematic work has been done to study the behavior of small groups as decision-making agents in markets and other strategic games. This may limit the relevance of both economics and its critics to the objective of developing an understanding of how most important decisions are made. In order to gain some insight into this issue, this paper compares group and individual economic behavior. The objective of the research is to learn whether there are systematic differences between decisions made by groups and individual agents in market environments characterized by risky outcomes. A quantitative measure of deviation from minimally-rational decisions is used to compare group and individual behavior in common value auctions.

On the existence of an increasing symmetric equilibrium in (k + 1)-st price common value auctions

In a classical result, Milgrom (1981a) established that the Monotone Likelihood Ratio Property (MLRP) is a sufficient condition for the existence of an increasing symmetric equilibrium in (k + 1)-st price common value auctions. We show: (1) If MLRP is violated, then for any number of bidders and objects there exists a distribution of the common value such that no increasing symmetric equilibrium exists; (2) If MLRP is violated, then for any distribution of the common value there exist infinitely many pairs of the number of bidders and the number of objects such that an increasing symmetric equilibrium does not exist; (3) There are examples where an increasing symmetric equilibrium exists even when the signal distribution violates MLRP.

Equilibrium in a Family of Common-Value First-Price Auctions with Differential Information

Equilibrium strategies are explicitly derived for a family of two-bidder common-value first-price auctions in which players have ex ante different information represented by finite partitions of the set of possible values for the object being sold. The distribution of bids for the ex post strong player stochastically dominates that for the ex post weak player. Comparison with the dominance-solvable equilibrium in a second-price auction shows the Milgrom-Weber finding that the second-price auction yields at least as much revenue as the first-price auction fails with asymmetry: in some cases the first-price auction provides greater expected revenue, in some cases less.

Level-k Auctions: Can a Nonequilibrium Model of Strategic Thinking Explain the Winner's Curse and Overbidding in Private-Value Auctions?

This paper proposes a structural nonequilibrium model of initial responses to incomplete-information games based on “level-k” thinking, which describes behavior in many experiments with complete-information games. We derive the model's implications in first- and second-price auctions with general information structures, compare them to equilibrium and Eyster and Rabin's (2005) “cursed equilibrium,” and evaluate the model's potential to explain nonequilibrium bidding in auction experiments. The level-k model generalizes many insights from equilibrium auction theory. It allows a unified explanation of the winner's curse in common-value auctions and overbidding in those independent-private-value auctions without the uniform value distributions used in most experiments.

Common value auctions with asymmetric bidder information

We study a first price auction with two asymmetric bidders. A unique generically asymmetric equilibrium exists under some conditions. Aggressive bidding is not necessarily associated with inferiority of information. Reduction in asymmetry can have an ambiguous effect on revenue.

When Less (Potential Demand) is More (Revenue): Asymmetric Bidding Capacities in Divisible Good Auctions

We show that asymmetry in bidders' capacity constraints plays an important role in inhibiting collusion and promoting competitive outcomes in multi-unit common value auctions. This effect seems to be related to the increased difficulty of coordination when there are fundamental differences between bidders. The discriminatory auction is shown to be more susceptible to collusion than is the uniform-price auction and consequently asymmetry in capacity constraints plays a more important role in the discriminatory auction. These results suggest that the revenue maximizing auction format may depend heavily on a variety of factors specific to particular auction settings.

Second-price common-value auctions under multidimensional uncertainty

The literature has demonstrated that second-price common-value auctions are sensitive to the presence of asymmetries among bidders. In a two-bidder model, Bikhchandani [1988. Reputation in repeated second-price auctions. J. Econ. Theory 46, 97–119] has shown that if it is common knowledge that one bidder has a disadvantage compared to her opponent, that bidder (almost surely) never wins the auction. Employing a similar two-bidder model, this paper shows that this result does not carry over when one allows for two-sided uncertainty. In such case, in every equilibrium, the disadvantaged type bidder needs to win the auction with strictly positive probability. We then solve for the equilibria in two cases, one with two types and another with a continuum of types, and we show that they converge to the symmetric equilibria of the corresponding symmetric auctions. We thus reestablish a lost linkage in the analysis of common-value and almost-common-value auctions.

Naive Bidding

This paper presents an equilibrium explanation for the persistence of naive bidding. Specifically, we consider a common value auction in which a “naive” bidder (who ignores the winner's curse) competes against a fully rational bidder. We show that the naive bidder earns higher equilibrium profits than the rational bidder when the signal distribution is symmetric and unimodal. We then consider a sequence of such auctions with randomly selected participants from a population of naive and rational bidders, with the proportion of bidder types in the population evolving in response to their relative payoffs in the auctions. We show that the evolutionary equilibrium contains a strictly positive proportion of naive bidders. Finally, we consider more general examples in which a naive bidder matched against a rational bidder does (i) worse than his rational opponent, but (ii) better than a rational bidder matched against another rational bidder. Again, the evolutionary equilibrium contains a strictly positive proportion of naive bidders. The results suggest that overconfident recent entrants in Internet and other low transaction-cost auctions of items that appeal to a mass audience may earn higher payoffs than their experienced competitors and, thus, will not eventually be driven from the market.

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, making analysis difficult. 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).

Selection Bias, Demographic Effects, and Ability Effects in Common Value Auction Experiments

Inexperienced women, along with economics and business majors, are much more susceptible to the winner's curse, as are subjects with lower SAT/ACT scores. There are strong selection effects in bid function estimates for inexperienced and experienced subjects due to bankruptcies and bidders who have lower earnings returning less frequently as experienced subjects. These selection effects are not identified using standard econometric techniques but are identified through experimental treatment effects. Ignoring these selection effects leads to misleading estimates of learning. (JEL D44, D83, J16)

Selection Bias, Demographic Effects and Ability Effects in Common Value Auction Experiments

We find clear demographic and ability effects on bidding in common value auctions: inexperienced women are much more susceptible to the winner's curse than men, controlling for SAT/ACT scores and college major; economics and business majors substantially overbid relative to other majors; and those with superior SAT/ACT scores are much less susceptible to the winner's curse, with the primary effect coming from those with below median scores doing worse, as opposed to those with very high scores doing substantially better, and with composite SAT/ACT score being a more reliable predictor than either math or verbal scores by themselves. There are strong selection effects in bid estimates for both inexperienced and experienced subjects that are not identified using standard econometric techniques but rather through our experimental design effects. Ignoring these selection effects is most misleading for inexperienced bidders, as the unbiased estimates of the bid function indicate much faster learning and adjustment to the winner's curse for individual bidders than do the biased estimates.

Randomization, endogeneity and laboratory experiments: the role of cash balances in private value auctions

From a theoretical perspective, cash balances are thought to play a role in common value auctions because of limited liability. However, they have also been found to be important in common value auctions where limited liability is not an issue. This paper investigates whether this effect carries over to private value auctions, since limited liability issues do not arise in private value auctions. We address the issue that cash balances are likely to be endogenous. We show that additional randomization can be used to reduce endogeneity problems and to improve the performance of our estimators. Further, we find that standard panel data econometric techniques are very useful in the analysis of data from laboratory experiments. Finally, we find that the cash balance effect does indeed carry over from common value auctions to private value auctions.

The Competitiveness of Joint Bidding in Multi-Unit Uniform-Price Auctions

Recent literature on joint bidding in a single-unit, Common-Value (CV) auction argues that the inference and precision that emerges from pooling information by joint bidders enhances competition. Such information pooling mitigates adverse selection and results in more aggressive bidding and may even increase revenue despite the reduction in the number of bidders. We analyze here, for the first time, joint bidding in a simple CV, uniform-price auction with multi-unit demand. This introduces an opposite force due to (increased) monopsony power of the joint bidders, called demand reduction (DR). We show that the pro-competitive benefit from joint bidding in single unit auctions does not generalize to a multi-unit environment, even when DR is disallowed. With DR, the scope for improved competition is further eroded.

Does observation influence learning?

A common value auction experiment is run to compare the relative influence of observation and experience on learning. It is shown that the ex-post observation of opponents' actions and payoffs homogenizes behavior and accelerates learning toward the Nash equilibrium. Additionally, experiential, and observational learning are both relevant and of comparable magnitude. A general reinforcement model for continuous strategies, encompassing choice reinforcement learning, direction learning and payoff dependent imitation, performs well in explaining the experimental data, and it dominates competing models such as the reinforcement of best response strategies.