Second-price Common-value Auctions Research Articles

Peaches, lemons, and cookies: Designing auction markets with dispersed information

We study how ex ante information asymmetries affect revenue in common-value second-price auctions, motivated by online advertising auctions where “cookies” inform individual advertisers about advertising opportunities. We distinguish information structures in which cookies identify “lemons” (low-value impressions) from those in which cookies identify “peaches” (high-value impressions). As this setting features multiple Nash equilibria, we introduce a new refinement, “tremble robust equilibrium” (TRE) and characterize the unique TRE in first-price and second-price common-value auctions with two bidders who each receive a binary signal. We find that common-value second-price auction revenues are vulnerable to ex ante information asymmetry if relatively rare cookies identify lemons, but not if they identify peaches. First-price auction revenues are substantially higher than second-price auction revenues under these conditions. Extensions show that these insights are robust.

Second-price common value auctions with uncertainty, private and public information: Experimental evidence

We conduct a laboratory experiment of second-price sealed bid auctions of a common value good with two bidders. Bidders face three different types of information: common uncertainty (unknown information), private information (known by one bidder) and public information (known by both bidders), and auctions differ on the relative importance of these three types of information. We find that subjects barely differentiate between private and public information and deviate from the theoretical predictions with respect to all three types of information. There is under-reaction to both private and public information and systematic overbidding in all auctions above and beyond the standard winner’s curse. The Cursed Equilibrium and Level-k models successfully account for some features of the data but others remain largely unexplained.

Goodwill Can Hurt: A theoretical and experimental investigation of return policies in auctions

Will generous return policies in auctions benefit bidders? We investigate this issue using second-price common-value auctions. Theoretically, we find that the symmetric bidding equilibrium is unique unless returns are free, and when returns are free there exist multiple equilibria with different implications for sellers. Moreover, more generous return policies mitigate the winner's curse, but also push the bids higher, thus hurting bidders by eroding their surplus. In the experiment, bids increase and bidders' earnings decrease with more generous return policies as predicted. With free returns, many bidders bid above the highest possible value, subsequently returning the item regardless of value. Though consistent with equilibrium behavior, this is not optimal for sellers.

Equilibrium Selection in Second-Price Common-Value Auctions

This paper considers the problem of equilibrium selection in a second-price auction with two bidders. We show that for each ex post equilibrium in continuous and undominated strategies of the auction, a sequence of almost common-value auctions can be constructed such that each of them possesses a unique undominated and continuous equilibrium and the corresponding sequence of equilibria converges to that ex post equilibrium. Therefore, no equilibrium selection of this model based on perturbations seems to be more convincing than others.

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.

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.

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.

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.

Comparative static effects of number of bidders and public information on behavior in second-price common value auctions

Comparative static tests of Nash bidding theory in second-price common value auctions show that bidders fail to respond in the right direction to more rivals and to public information concerning the value of the item. The former provides a clear indication that bidders fail to appreciate the adverse selection forces inherent in common value auctions, while the latter shows that policy prescriptions can fail given out-of-equilibrium behavior. These tests of Nash bidding theory apply to a far wider variety of circumstances than in first-price auctions, so there is less scope to rationalize the failure of the theory.