Common Value Auctions Research Articles

Auction prices, market share, and a common agent

The primary pro-competitive justification for multiple principals to hire a common bidding agent is efficiency. The efficiency gained by doing so increases the advantage of the common bidding agent. Almost common value auction theory predicts that an advantaged bidder is able to reduce competition by credibly enhancing the ‘winner's curse’ of disadvantaged rivals. The credible threat results in disadvantaged rivals exiting the bidding process early, leaving the advantaged bidder to purchase most, if not all, units at lower prices than when rivals have common values. The results of our empirical study of a common bidding agent are consistent with this theory.

Auction Prices, Market Share, and a Common Agent

The primary pro-competitive justification for multiple principals to hire a common bidding agent is efficiency. The efficiency gained by doing so increases the advantage of the common bidding agent. Almost common value auction theory predicts that an advantaged bidder is able to reduce competition by credibly enhancing the ‘winner’s curse’ of disadvantaged rivals. The credible threat results in disadvantaged rivals exiting the bidding process early, leaving the advantaged bidder to purchase most, if not all, units at lower prices than when rivals have common values. The results of our empirical study of a common bidding agent are consistent with this theory.

Bayesian Inference in Structural Second-Price Common Value Auctions

Structural econometric auction models with explicit game-theoretic modeling of bidding strategies have been quite a challenge from a methodological perspective, especially within the common value framework. We develop a Bayesian analysis of the hierarchical Gaussian common value model with stochastic entry introduced by Bajari and Hortaçsu. A key component of our approach is an accurate and easily interpretable analytical approximation of the equilibrium bid function, resulting in a fast and numerically stable evaluation of the likelihood function. We extend the analysis to situations with positive valuations using a hierarchical gamma model. We use a Bayesian variable selection algorithm that simultaneously samples the posterior distribution of the model parameters and does inference on the choice of covariates. The methodology is applied to simulated data and to a newly collected dataset from eBay with bids and covariates from 1000 coin auctions. We demonstrate that the Bayesian algorithm is very efficient and that the approximation error in the bid function has virtually no effect on the model inference. Both models fit the data well, but the Gaussian model outperforms the gamma model in an out-of-sample forecasting evaluation of auction prices. This article has supplementary material online.

Market composition and experience in common-value auctions

This study investigates whether market composition affects individual bidding and the aggregate market in first-price sealed-bid common-value auctions. It compares all-inexperienced markets with only inexperienced bidders, all-experienced markets with only experienced bidders, and mixed markets with both types. On average, there is no market-composition effect for both experienced and inexperienced bidders. When controlling for gender, a market-composition effect appears for inexperienced subjects: Men bid more aggressively in mixed than in all-inexperienced markets, and women bid more aggressively in all-inexperienced markets. On the aggregate level, the all-inexperienced market is the most aggressive with highest winning bids; the all-experienced market is the least aggressive. The mixed market is in between: Both experienced and inexperienced win auctions in this market, but experienced bidders win less auctions than they should.

Equilibrium and revenue in a family of common-value first-price auctions with differential information

We study a discrete common-value auction environment with two asymmetrically informed bidders. Equilibrium of the first-price auction is in mixed strategies, which we characterize using a doubly recursive solution method. The distribution of bids for the ex post strong player stochastically dominates that for the ex post weak player. This result complements Maskin and Riley’s (Rev Econ Stud 67:413–438, 2000) similar result for asymmetric private-value auctions. Finally, comparison with the dominance-solvable equilibrium in a second-price auction shows the Milgrom–Weber (Econometrica 50:1089–1122, 1982a) 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.

Bidding off the wall in common value auctions

This paper examines the practice of phantom bidding in common value auctions with asymmetric information. Unlike in private value auctions it is very difficult to profit from phantom bidding even if the auctioneer observes the number of interested bidders. We find that the auctioneer is worse off submitting low bids or mixing between his participation strategies. Phantom bidding can generate higher revenues if a single bidder with a high value estimate is likely to be present at the auction. Systematic observation of an isolated high estimate requires negative correlation across bidders’ information that is atypical in a common value environment.

Dominance-solvable common-value large auctions

We consider second-price common-value auctions with an increasing number of bidders. We define a strategy of bidder i to be ( ex-post, weakly) asymptotically dominated if there is another strategy for i that does, in the limit, as well against any sequence of strategies of iʼs opponents, and with positive probability does strictly better against at least one sequence. Our main result provides a sufficient condition on the information structure for the process of iteratively deleting asymptotically dominated strategies to terminate after just two iterations, with only one strategy left for each player. This strategy is fully characterized. We also show that, under standard assumptions, a similar condition to that of Wilson (1977) implies our sufficient condition and therefore implies asymptotic dominance solvability.

An experimental investigation of entry cost effects in sealed-bid dollar auctions

We experimentally study the effect of entry costs on bidding and entry behavior in common value auctions. We find, with entry costs, players bid lower in first price and higher in second price auctions, compared to no entry fee auctions.

Almost Common Value Auctions and Discontinuous Equilibria

In almost common value auctions, even a very small private payoff advantage is usually supposed to have an explosive effect on the outcomes in a second-price sealed-bid common value auction. According to Bikhchandani (1988) and Klemperer (1998) the large set of equilibria obtained for common value auction games drastically shrinks, so that the advantaged player always wins the auction, at a price that sharply decreases the seller’s payoff. Yet this result has not been observed experimentally. In this paper, we show that Bikhchandani’s equilibria are not the only equilibria of the game. By allowing bids to not continuously depend on private information, we establish a new family of perfect equilibria with nice properties: (i) the advantaged bidder does no longer win the auction regardless of her private information, (ii) she may pay a much higher price than in Bikhchandani’s equilibria, (iii) there is no ex-post regret for both the winner and the looser, and (iv) the equilibria give partial support to some naive behaviour observed experimentally. Moreover the intersection between these equilibria, level-k reasoning and cursed equilibria is not empty.

Single object auctions with interdependent values

This paper reviews single object auctions when bidders? values of the object are interdependent. We will see how the auction forms could be ranked in terms of expected revenue when signals that bidders have about the value of the object are affiliated. In the discussion that follows we will deal with reserve prices and entry fees. Furthermore we will examine the conditions that have to be met for English auction with asymmetric bidders to allocate the object efficiently. Finally, common value auctions will be considered when all bidders have the same value for the object.

An experimental study of auctions with a buy price under private and common values

eBayʼs Buy It Now format allows a seller to list an auction with a “buy price” at which a bidder may purchase the item immediately and end the auction. When bidders are risk averse, then theoretically a buy price can raise seller revenue when values are private (but not when values are common). We report the results of laboratory experiments designed to determine whether in practice a buy price is advantageous to the seller. We find that a suitably chosen buy price yields a substantial increase in seller revenue when values are private, and a small (but statistically insignificant) increase in revenue when values are common. In both cases a buy price reduces the variance of seller revenue. A behavioral model which incorporates the winnerʼs curse and the overweighting by bidders of their own signal explains the common value auction data better than the rational model.

Core-Stable Rings in Second Price Auctions with Common Values

In a common value auction in which the information partitions of the bidders are connected, all rings are core-stable. More precisely, the ex ante expected utilities of rings, at the (noncooperative) sophisticated equilibrium proposed by Einy, Haimanko, Orzach and Sela (Journal of Mathematical Economics, 2002), describe a cooperative game, in characteristic function form, in spite of the underlying strategic externalities. A ring is core-stable if the core of this characteristic function is not empty. Furthermore, every ring can implement its sophisticated equilibrium strategy by means of an incentive compatible mechanism.

Bayesian Inference in Structural Second-Price Common Value Auctions

Structural econometric auction models with explicit game-theoretic modeling of bidding strategies have been quite a challenge from a methodological perspective, especially within the common value framework. We develop a Bayesian analysis of the hierarchical Gaussian common value model with stochastic entry introduced by Bajari and Hortacsu (2003). A key component of our approach is an accurate and easily interpretable analytical approximation of the equilibrium bid function, resulting in a fast and numerically stable evaluation of the likelihood function. The analysis is also extended to situations with positive valuations using a hierarchical Gamma model. We use a Bayesian variable selection algorithm that simultaneously samples the posterior distribution of the model parameters and does inference on the choice of covariates. The methodology is applied to simulated data and to a carefully collected dataset from eBay with bids and covariates from 1000 coin auctions. It is demonstrated that the Bayesian algorithm is very efficient and that the approximation error in the bid function has virtually no effect on the model inference. Both models fit the data well, but the Gaussian model outperforms the Gamma model in an out-of-sample forecasting evaluation of auction prices.

Common Value vs. Private Value Categories in Online Auctions: A Distinction Without a Difference?

There is a growing body of empirical research that attempts to distinguish private value from common value auctions. Strategic behavior for a seller/bidder in these two paradigms should differ, so the assumption of, or the identification of, the type of auction (private or common) is important for understanding the auction dynamics and strategies in game-theoretic models. However, it is difficult to recognize which of the two paradigms applies to a particular good. In this article, we briefly review some of the empirical work distinguishing common/private values using observed bidding behavior, both structural nonparametric and parametric models of auctions. We then examine the use of a priori beliefs to classify product categories. Specifically, we survey auction experts on their subjective judgment in classifying a list of consumer product categories on a private/common value continuum. We also survey consumers, asking them their subjective assessment. Interestingly, not only are extant models unable empirically to distinguish between private value and common value auctions, but also the experts have strongly divergent opinions on classifying product categories on this continuum. These findings raise doubts about the appropriateness of using a priori beliefs to classify a product as a common value versus a private value, and furthermore the findings question the feasibility of game-theoretic models to empirically distinguish private value from common value auctions. Perhaps decision theory would be a more useful paradigm for modeling auction decisions in practice.

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.

Reserve Prices in Common-Value Auctions with Asymmetrically Informed Bidders

In this paper, I study common-value auctions with two asymmetrically informed bidders and a reserve price. First, I consider a static auction in which one bidder has perfect information about the value of the object and the other does not have any private information. I derive the optimal reserve price and find that the optimal reserve price is always lower in a static common-value auction with asymmetrically informed bidders than in a standard independent-private-value (SIPV) auction. I then consider a dynamic auction in which an informed bidder obtains private information in two consecutive periods. I characterize a set of equilibria in which the strategy of the informed bidder is to decide whether to bid or to wait until the second period, while the uninformed bidder randomizes his bid, if he bids in the first period, and never bids in the second period. I show that, as long as the uninformed bidder does not have a mass point at the reserve price, the optimal reserve price can be characterized so that it is analogous to the optimal reserve price for the static auction. In addition, I compare the dynamic auction with the first period auction (the seller commits to sell the object in only the first period) and provide conditions under which one auction outperforms the other.

Can Relaxation of Beliefs Rationalize the Winner's Curse?: An Experimental Study

We use a second-price common-value auction, called the maximal game, to experimentally study whether the winner's curse (WC) can be explained by models which retain best-response behavior but allow for inconsistent beliefs. We compare behavior in a regular version of the maximal game, where the WC can be explained by inconsistent beliefs, to behavior in versions where such explanations are less plausible. We find little evidence of differences in behavior. Overall, our study casts a serious doubt on theories that posit the WC is driven by beliefs.

Asymmetric common-value auctions with applications to private-value auctions with resale

We study a model of common-value auctions with two bidders in which bidders’ private information are independently and asymmetrically distributed. We present sufficient and necessary conditions, respectively, under which the expected revenues from first-price and second-price auctions can be ranked. Using these conditions and a bid-equivalence between common-value auctions and private-value auctions with resale, we extend the revenue-ranking result of Hafalir and Krishna [Am Econ Rev 98, 2008a] and provide necessary conditions for their ranking to hold. In addition, we provide sufficient and necessary conditions for the opposite ranking of revenues, respectively. Our analysis helps clarify the roles of two forms of regularity assumptions (buyer-regularity and seller-regularity) in ranking revenues and illustrates how revenue ranking is linked to submodularity and supermodularity of the common-value function and to a single-crossing property of a function derived from the monopoly or monopsony pricing function in the resale stage.

Entry and Bidding in Common and Private Value Auctions with an Unknown Number of Rivals

In many procurement auctions bidders do not know how many rivals they face at the time that they incur the cost of preparing their bids. We show in a theoretical model that regardless of whether the procurement is characterized by private or by common values an increase in the potential number of bidders may lead to higher procurement costs. This raises potential policy questions of whether and how entry should be encouraged or limited in public procurement auctions. We use evidence from auctions of construction contracts to estimate the effect of an increase in the pool of potential bidders on entry and auction prices when entry and bidding decisions are made sequentially with no knowledge of the number or identity of the actual competitors.

Revenue comparison in common-value auctions: Two examples

When players' affiliated values are symmetrically distributed, expected revenue in the second-price auction equals or exceeds that in the first-price auction (Milgrom and Weber, 1982). We provide two common-value examples where this ranking fails when players are asymmetrically informed.