Individual behavior of first-price auctions: The importance of information feedback in computerized experimental markets

This article reports the results of an individual choice experiment designed to test the Nash equilibrium predictions of the first-price sealed-bid auction. A subject faced in 100 auctions always the same resale value and competed with computer-simulated bids. The design used between-subjects variation and involved information feedback as the treatment variable. Earlier experimental work on first price auctions has frequently reported an overbidding relative to the risk neutral Nash equilibrium. Our data provide evidence that overbidding can be fostered by the standard information feedback in auction experiments, which, after each auction, reveals the winning bid only. By means of learning direction theory we explain the individual bidding dynamics in our experiment. Finally we apply impulse balance theory and make long run predictions of individual bidding behavior.     

Market behavior in bid,offer, and double auctions: A Reexmination

This study examines the robustness of the previously observed [Smith (1964)] differences in market behavior between double auctions (both buyers and sellers may enter price quotes), bid auctions (only buyers may enter price quotes), and offer auctions (only sellers may enter price quotes). Based on the results of twenty-one market experiments, we find little support for the a priori hypothesis that bid auction prices tend to be greater than double auction prices which tend to be greater than offer auction prices.     

Temporary partnership and subcontracting: Pre- vs. post- award outsourcing in public procurement

We empirically compare bids (i.e. prices) from temporary partnerships (TPs), that outsource part of the contract before the auction, and firms that outsource afterwards. Using a comprehensive dataset on procurement auctions for public works in Valle d’Aosta (Italy), we find that the timing of outsourcing affects the bids and the probability of winning the auction. Specifically, TPs bid closer to the payoff maximizing offer and are more likely to win. Hence, the price paid by the public buyer is lower. These results are supported by a simple theoretical setting showing that, by pre-committing to a TP, suppliers have a lower risk of being “held up” by subcontractors than firms that outsource part of the work after the bidding phase. Our results show the advantage for TPs of freely choosing partners, size and boundaries before the auction, highlighting their potential in fostering the effective participation in public procurement procedures of Small and Medium-sized Enterprises (SMEs).     

Hybrid allocation mechanisms for publicly provided goods

Motivated by efficiency and equity concerns, public resource managers have increasingly utilized hybrid allocation mechanisms that combine features of commonly used price (e.g., auction) and non-price (e.g., lottery) mechanisms. This study serves as an initial investigation of these hybrid mechanisms, exploring theoretically and experimentally how the opportunity to obtain a homogeneous good in a subsequent lottery affects Nash equilibrium bids in discriminative and uniform price auctions. The lottery imposes an opportunity cost to winning the auction, systematically reducing equilibrium auction bids. In contrast to the uniform price auction, equilibrium bids in the uniform price hybrid mechanism vary with bidder risk preferences. Experimental evidence suggests that the presence of the lottery and risk attitudes (elicited through a preceding experiment) impact auction bids in the directions predicted by theory. Finally, we find that theoretically and experimentally, the subsequent lottery does not compromise the efficiency of the auction component of the hybrid mechanisms.     

Investment Incentives in Procurement Auctions

This paper investigates firms' incentives to invest in cost reduction in the first price sealed bid auction, a format largely used for procurement. Two central features of the model are that we allow firms to be heterogeneous and that investment is observable. We find that firms will tend to underinvest in cost reduction because they anticipate fiercer head-on competition. Using the second price auction as a benchmark, we also find that the first price auction will elicit less investment from market participants and that this is socially inefficient. These results have implications for market design when investment is important.     

The high/low divide: Self-selection by values in auction choice

Most prior theoretical and experimental work involving auction choice has assumed bidders find out their value after making a choice of which auction to enter. We examine whether or not bidders knowing their value prior to making a choice of which among multiple alternative auction formats to enter impacts their choice decision and/or the outcome of the auctions. The results show a strong impact on auction choice. Subjects with low values choose the first price sealed bid auction more often while subjects with high values choose the ascending auction more often. The number of bidders in each auction, revenue, efficiency and average bidder surplus all end up equalized.     

Cost overrun and auction format in small size public works

We study the effect on cost overruns of two different auction formats, the first price sealed bid and the average bid, conditional on whether entry is open or restricted. The first price format awards the contract to the lowest bid, while the average bid format awards the contract to the bid closest to the average of all the bids. This latter format is supposed to prevent an unreliable low bidder from winning the auction; as a consequence cost overruns should be lower under the average bid than under the first price format. We test this hypothesis with a panel data set of auctions held in the Italian Veneto region between 2004 and 2006, including small size public projects in sectors such as road works and building maintenance. We find that cost overruns are lower under the average bid format, but only when the entry is restricted. We then speculate on possible explanations for this result.     

Asymptotic and small sample analysis of the stochastic properties and certainty equivalents of winning bids in independent private values auctions$\!$

Summary. This paper investigates the stochastic properties of the first price and second price winning bids in auctions with risk neutral bidders with independent and identically distributed valuations. In such an environment, the winning first price bids second order stochastically dominate the second price winning bids. A key result of this paper is that the ratio of the variance of the winning first price bid to that of the winning second price bid is strictly less than one even as the number of bidders goes to infinity. This suggests that the stochastic dominance of the winning first price bids does not vanish even in the limit. Both the asymptotic and small sample properties of winning bids are investigated. In particular, the small sample results suggest that the identification power of econometric procedures that rely on winning bids can decline rapidly as the number of bidders increases. This paper also includes a systematic evaluation of the difference in certainty equivalents between the two auction formats for several common distributions and number of bidders for the case of auctioneers with constant coefficient of absolute risk aversion. These results are presented in a form that makes it easy to apply them to a specific auction of interest.Received: 15 July 2002, Revised: 7 April 2003, JEL Classification Numbers: D44.I would like to thank David Pearce for helpful comments and discussion and a referee for suggestions that have greatly improved this paper.     

The effect of randomized school admissions on voter participation

There is little causal evidence on the effect of economic and policy outcomes on voting behavior. This paper uses randomized outcomes from a school choice lottery to examine if lottery outcomes affect voting behavior in a school board election. We show that losing the lottery has no significant impact on overall voting behavior; however, among white families, those with above median income and prior voting history, lottery losers were significantly more likely to vote than lottery winners. Using propensity score methods, we compare the voting of lottery participants to similar families who did not participate in the lottery. We find that losing the school choice lottery caused an increase in voter turnout among whites, while winning the lottery had no effect relative to non-participants. Overall, our empirical results lend support to models of expressive and retrospective voting, where likely voters are motivated to vote by past negative policy outcomes.     

Bidding ‘as if’ risk neutral in experimental first price auctions without information feedback

Experimental research on first price sealed bid auctions has usually involved repeated settings with information feedback on winning bids and payoffs after each auction round. Relative to the risk neutral Nash equilibrium, significantly higher bidding has been reported. The present paper reports the results of experimental first price auctions with n=7 where feedback on payoffs and winning bids is withheld. Under these conditions, average bidding is below the risk neutral Nash equilibrium prediction but converges to it with repetition.

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Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.      

Valuation structure in first-price and least-revenue auctions: an experimental investigation

In many auctions the valuation structure involves both private and common value elements. Existing experimental evidence (e.g. Goeree and Offerman in Am. Econ. Rev. 92(3):625–643, 2002) demonstrates that first-price auctions with this valuation structure tend to be inefficient, and inexperienced subjects tend to bid above the break-even bidding threshold. In this paper, we compare first-price auctions with an alternative auction mechanism: the least-revenue auction. This auction mechanism shifts the risk regarding the common value of the good to the auctioneer. Such a shift is desirable when ex post negative payoffs for the winning bidder results in unfulfilled contracts, as is often the case in infrastructure concessions contracts. We directly compare these two auction formats within two valuation structures: (1) pure common value and (2) common value with a private cost. We find that, relative to first-price auctions, bidding above the break-even bidding threshold is significantly less prevalent in least-revenue auctions regardless of valuation structure. As a result, revenue in first-price auctions is higher than in least-revenue auctions, contrary to theory. Further, when there are private and common value components, least-revenue auctions are significantly more efficient than first-price auctions.     

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.     

Second chance offers in auctions

This paper examines situations in which a seller might make a second chance (take-it-or-leave-it) offer to a non-winning bidder at a price equal to their bid at auction. This study is motivated by the take-it-or-leave-it second chance offer rules used by eBay and a number of state procurement agencies. Equilibrium bidder behavior is determined for IPV sealed bid first price, second price, English, and Vickrey auctions when a second chance offer will be made with an exogenous probability $p$ . In all but the Vickrey auction (which elicits the dominant strategy of bidding one’s value) equilibrium bids are lower than if there were no possibility of a second chance offer and higher than if a second chance offer will be made for certain. Further, the possibility of a second chance offer erodes the strategic equivalence between second price bids and English auction drop out levels. If bidders are risk averse (with CRRA preferences), this difference leads to expected revenue dominance of the second price over the English auction, both of which dominate the Vickrey auction. The first price auction is also shown to revenue dominate the Vickrey auction, and moreover, numerical results and intuition from existing literature suggest that the first price auction revenue dominates the second price auction.     

A choice of auction format in seller cheating: a signaling game analysis

In this paper, we examine which auction format, first-price or second-price, a seller will choose when he can profitably cheat in a second price auction by observing all bids by possible buyers and submitting a shill bid as pretending to be a buyer. We model this choice of auction format in seller cheating as a signaling game in which the buyers may regard the selection of a second price auction by the seller as a signal that he is a shill bidder. By introducing trembling-hand perfectness as a refinement of signaling equilibrium, we find two possible strictly perfect signaling equilibria. One is a separating equilibrium in which a noncheating honest seller selects a first price auction and a cheating seller does a second price auction. In another pooling equilibrium, however, both cheating and non-cheating sellers select a second price auction. The conclusion that a seller chooses a second price auction even if he cannot cheat is in contrast to the previous literature, which focused on the case of independent values. We thank an anonymous referee for useful comments that have improved the paper. This research was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (B) 15310023 and (C) 18530139.     

Simultaneous use of auctions and posted prices

I consider a model in which several identical objects are sold simultaneously via an auction and a posted price mechanism. The model explains several empirical regularities regarding bidding behavior in eBay auctions such as the finding that some bidders bid multiple times over the course of the auction, and that bidders tend to bid with greater frequency near the end of the auction than the beginning. I also show that sellers prefer to simultaneously use auctions and posted prices than to use either mechanism individually.     

Bidding behavior in competing auctions: Evidence from eBay

Much of the existing auction literature treats auctions as running independently of one another, with each bidder choosing to participate in only one auction. However, in many online auctions, a number of substitutable goods are auctioned concurrently and bidders can bid on several auctions at the same time. Recent theoretical research shows how bidders can gain from the existence of competing auctions, the current paper providing the first empirical evidence in support of competing auctions theory using online auctions data from eBay. Our results indicate that a significant proportion of bidders do bid across competing auctions and that bidders tend to submit bids on auctions with the lowest standing bid, as the theory predicts. The paper also shows that winning bidders who cross-bid pay lower prices on average than winning bidders who do not.     

The role of varying risk attitudes in an auction with a buyout option

Summary. An auction with a buyout option is modelled. Such an option allows a bidder to purchase the item being auctioned at a pre-specified buyout price, instead of attempting to obtain the item through the traditional auction procedure. This analysis is motivated by internet auctions where such options are present. If all auction participants are risk neutral, the seller will choose a buyout price high enough so that the option is never exercised. However, a risk averse seller facing risk neutral bidders will choose a price low enough so that the option is exercised with positive probability. Further, if bidders are risk neutral and the seller is risk averse, this option may result in a Pareto improvement compared to a sealed bid second price auction.Received: 3 December 2002, Revised: 28 September 2004, JEL Classification Numbers: D44, L86, D8. Correspondence to: Timothy MathewsWe would like to thank Yair Tauman, Thomas Jeitschko, Pradeep Dubey, Konstantinos Serfes, Abraham Neyman, Qihong Liu, and an anonymous referee, as well as participants of the 2001 Canadian Economic Association Conference and the 2001 Stony Brook International Conference on Game Theory. This paper is based upon Chapter Two of Mathews doctoral dissertation.     

SUBJECTIVE PROBABILITIES IN GAMES: AN APPLICATION TO THE OVERBIDDING PUZZLE*

This article illustrates how the joint elicitation of subjective probabilities and preferences may help us understand behavior in games. We conduct an experiment to test whether biased probabilistic beliefs may explain overbidding in first‐price auctions. The experimental outcomes indicate that subjects underestimate their probability of winning the auction, and indeed overbid. When provided with feedback on the precision of their predictions, subjects learn to make better predictions, and to curb significantly overbidding. The structural estimation of different behavioral models suggests that biased probabilistic beliefs are a driving force behind overbidding, and that risk aversion plays a lesser role than previously believed.     

Sequential vs. single-round uniform-price auctions

We study sequential and single-round uniform-price auctions with affiliated values. We derive symmetric equilibrium for the auction in which k₁ objects are sold in the first round and k₂ in the second round, with and without revelation of the first-round winning bids. We demonstrate that auctioning objects in sequence generates a lowballing effect that reduces the first-round price. Total revenue is greater in a single-round, uniform auction for k=k₁+k₂ objects than in a sequential uniform auction with no bid announcement. When the first-round winning bids are announced, we also identify a positive informational effect on the second-round price. Total expected revenue in a sequential uniform auction with winning-bids announcement may be greater or smaller than in a single-round uniform auction, depending on the model's parameters.     

Competition in the economic crisis: Analysis of procurement auctions

We study the effects of the recent economic crisis on firms׳ bidding behavior and markups in sealed bid auctions. Using data from Austrian construction procurements, we estimate bidders׳ construction costs within a private value auction model. We find that markups of all bids submitted decrease by 1.5 percentage points in the recent economic crisis, markups of winning bids decrease by 3.3 percentage points. We also find that without the government stimulus package this decrease would have been larger. These two pieces of evidence point to pro-cyclical markups.