Collusion in one-shot second-price auctions

Summary. Most of the literature on collusive behavior in auctions ignores two important issues that make collusion difficult to sustain at least in one-shot interactions: the detection of cheating and the verification of bids. Colluding bidders may deceive each other by using shill bidders. Also, if the identities of the bidders and their bids are not published then it would be difficult to verify the bid of a colluding bidder. This paper addresses these problems in one shot second price auctions where one bidder offers another bidder a side payment in exchange for not participating in the auction, while the number of other bidders is stochastic. In spite of the barriers to collusion mentioned above, a simple side payment mechanism which depends only on the auction price is introduced. It induces a successful collusion, eliminates the verification problem, provides no incentive for the use of shill bidders and guarantees that the proponent obtains ex-post non-negative payoff. The colluding bidders are ex-ante strictly better off compared with the competitive case, irrespective of their types.Received: 27 November 2002, Revised: 28 January 2005, JEL Classification Numbers: C72, D44, D82.Yair Tauman: Correspondence toWe would like to thank an anonymous referee for very valuable comments and suggestions that significantly improved the paper. We thank Shmuel Zamir for a helpful discussion.     

Unraveling in first-price auction

In a private values first-price auction with random number of bidders, the auctioneer has to decide whether to announce or not the actual number of bidders. If the auctioneer cannot commit to any particular announcement policy, then he would like to reveal when the number of bidders is high in order to increase bidding competition. By the same logic, the auctioneer should like to conceal if the number turns out to be small. When bidders' types are independent, full revelation by the auctioneer is shown to be a unique equilibrium with ‘skeptical belief’ as the unique equilibrium belief.     

Allocating multiple units

Summary. This paper studies the allocation and rent distribution in multi-unit, combinatorial-bid auctions under complete information. We focus on the natural multi-unit analogue of the first-price auction, where buyers bid total payments, pay their bids, and where the seller allocates goods to maximize his revenue. While there are many equilibria in this auction, only efficient equilibria remain when the truthful equilibrium restriction of the menu-auction literature is used. Focusing on these equilibria we first show that the first-price auction just described is revenue and outcome equivalent to a Vickrey auction, which is the multi unit analogue of a second-price auction. Furthermore, we characterize these equilibria when valuations take a number of different forms: diminishing marginal valuations, increasing average valuations, and marginal valuations with single turning points. Received: December 23, 1999; revised version: December 10, 2001     

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.     

Second chance offers versus sequential auctions: theory and behavior

Second chance offers in online marketplaces involve a seller conducting an auction for a single object and then using information from the auction to offer a losing bidder a take-it-or-leave-it price for another unit. We theoretically and experimentally investigate this practice and compare it to two sequential auctions. We show that the equilibrium bidding strategy in the second chance offer mechanism only exists in mixed strategies, and we observe that this mechanism generates more profit for the auctioneer than two sequential auctions. We also observe virtually no rejections of profitable offers in the ultimatum bargaining stage.      

An elementary proof of the common maximal bid in asymmetric first-price and all-pay auctions

We prove that the maximal bid in asymmetric first-price and all-pay auctions is the same for all bidders. Our proof is elementary, and does not require that bidders are risk neutral, or that the distribution functions of their valuations are independent or smooth.     

The value of information in asymmetric all-pay auctions

This note analyzes a two-player all-pay auction with incomplete information. More precisely, one bidder is uncertain about the size of the initial advantage of his rival modeled as a head start in the auction.I derive the unique Bayesian Nash equilibrium outcome for a large class of cumulative distribution functions of the head start. The stronger player generates an informational rent if and only if his head start distribution is not stochastically dominated by a uniform distribution. I identify why my results for an uncertain head start differ qualitatively from uncertainty about a cost function or a valuation.     

Asymmetry and revenue in first-price auctions

We show by an example that in first-price IPV auctions, asymmetry in bidders' valuations need not reduce the revenue compared to a benchmark symmetric model with the same amount of social surplus. Asymmetry need not reduce competition in first-price auctions.     

Multilateral bargaining: conditional and unconditional offers

Summary. We present a game in which n persons split a cake, where a distinction between conditional and unconditional offers is made. This distinction sheds light on the contrasting results obtained in the previous literature of multilateral bargaining. By allowing the proposer to make both conditional and unconditional offers, we show that the game has a unique subgame perfect Nash equilibrium outcome. Received: March 14, 2000; revised version: March 13, 2001     

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.     

The effect of corruption on bidding behavior in first-price auctions

When the owner of an object sells it through an auction run by an agent of hers, corruption may appear. In a first-price auction, corruption can make honest bidders more or less aggressive, or their behavior can remain unchanged. We identify sufficient conditions for each of the three possibilities. We analyze the effects of corruption on efficiency, bidders’ welfare and expected revenue. Our results apply as well to the situation—unrelated to corruption—where one of the bidders is granted a right of first refusal.     

Revenue in first-price auctions with a buy-out price and risk-averse bidders

Journal of Economics - We model the “Buy-It-Now or Best Offer” eBay listing option as a first-price auction with a buy-out price and consider seller revenue when bidders are...     

Ratifiability of efficient collusive mechanisms in second-price auctions with participation costs

We investigate whether efficient collusive bidding mechanisms are affected by potential information leakage from bidders' decisions to participate in them within the independent private values setting. We apply the concept of ratifiability introduced by Cramton and Palfrey [Cramton, P.C., Palfrey, T.R., 1995, Ratifiable mechanisms: Learning from disagreement, Games Econ. Behav. 10 (2), 255–283] and show that when the seller uses a second-price auction with participation costs, the standard efficient cartel mechanisms such as pre-auction knockouts analyzed in the literature will not be ratified by cartel members. A high-value bidder benefits from vetoing the cartel mechanism since doing so sends a credible signal that she has high value, which in turn discourages other bidders from participating in the seller's auction.     

Uniqueness of equilibrium in sealed high-bid auctions

For the case of two buyers we show that equilibrium in the sealed high-bid auction is unique when (i) buyers' reservations prices are drawn independently from distributions with finite support and positive mass at the lower endpoint; (ii) buyers have private values; and (iii) buyers' preferences are log supermodular. For more than two buyers, we obtain the same result under the additional assumptions that (iv) buyers with the same reservation price have the same preferences; (v) buyers are risk neutral or risk averse with non-increasing absolute risk aversion; and (vi) the supports of the different buyers' distributions of reservation prices have the same upper endpoint.     

Strategic price discounting and rationing in uniform price auctions

I modify the uniform-price auction rules in allowing the seller to ration bidders. This allows me to provide a strategic foundation for underpricing when the seller has an interest in ownership dispersion. Moreover, many of the so-called “collusive-seeming” equilibria disappear.     

Entry decisions and bidding behavior in sequential first-price procurement auctions: An experimental study

Though many real life auctions are run independently of each other, from the bidders' point of view they often form sequences of auctions. We investigate how behavior responds to the additional incentives that are present in such auction sequences. Comparing subjects' decisions in single first-price procurement auctions with their decisions in a game consisting of two subsequent first-price procurement auctions, we find that, in line with the theoretical prediction, entry and bidding behavior is crucially affected by the opportunity cost of early bid submission. Though, entry decisions and average bids in the auction sequence systematically deviate from the perfect Bayesian equilibrium prediction. While the nature of the opponent (human being or computer) has no significant effect on these findings, giving subjects additional feedback on winners and prices seems to reduce the deviations from the equilibrium prediction.     

Trust,reputation and bidding behaviour in online mystery auctions

We use transactions from a distinctive online environment of ‘mystery’ auctions to examine the role that trust plays and how it impacts bidding behaviour when the exact characteristics of a good being auctioned are purposefully concealed from buyers. We show that buyers are generally trusting seller claims in online transactions and that seller reputation becomes significantly more important to buyers (as demonstrated by their bids) when the quality (or value) of the good is unspecified. Our findings can be extrapolated to consider broader economic implications of bidding behaviour impacted by trust, such as in financial markets, where over-bidding may lead to price bubbles.