Bidding for the future: signaling in auctions with an aftermarket

This paper considers auctions where bidders compete for an advantage in future strategic interactions. When bidders wish to exaggerate their private information, equilibrium bidding functions are biased upwards as bidders attempt to signal via the winning bid. Signaling is most prominent in second-price auctions where equilibrium bids are “above value.” In English and first-price auctions, signaling is less extreme since the winner incurs the cost of her signaling choice. The opportunity to signal lowers bidders’ payoffs and raises revenue. When bidders understate their private information, separating equilibria need not exist and the auction may not be efficient.     

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.     

All equilibria of the multi-unit Vickrey auction

This paper completely characterizes the set of equilibria of the Vickrey auction for multiple identical units when buyers have non-increasing marginal valuations and there are at least three potential buyers. There are two types of equilibria: In the first class of equilibria there are positive bids below the maximum valuation. In this class, above a threshold value all bidders bid truthfully on all units. One of the bidders bids at the threshold for any unit for which his valuation is below the threshold; the other bidders bid zero in this range. In the second class of equilibria there are as many bids at or above the maximum valuation as there are units. The allocation of these bids is arbitrary across bidders. All the remaining bids equal zero. With any positive reserve price equilibrium becomes unique: Bidders bid truthfully on all units for which their valuation exceeds the reserve price.     

A model of collateral, investment, and adverse selection

This paper characterizes the relationship between entrepreneurial wealth and aggregate investment under adverse selection. Its main finding is that such a relationship need not be monotonic. In particular, three results emerge from the analysis: (i) pooling equilibria, in which investment is independent of entrepreneurial wealth, are more likely to arise when entrepreneurial wealth is relatively low; (ii) separating equilibria, in which investment is increasing in entrepreneurial wealth, are most likely to arise when entrepreneurial wealth is relatively high and; (iii) for a given interest rate, an increase in entrepreneurial wealth may generate a discontinuous fall in investment.     

Non-bidding equilibrium in an ascending core-selecting auction

This paper investigates the perfect Bayesian equilibrium in an ascending-price core-selecting auction, which is recently used in some countries? spectrum license auctions. We suppose that there are two identical items, two small bidders, and one large bidder. The small bidders demand only one unit of the item, whereas the large bidder wants both units. Package bidding ensures that the large bidder faces no exposure problem and behaves truthfully. However, one of the small bidders stops bidding at the beginning in the equilibrium. Although small bidders generally face the free-rider problem and have incentives to underbid, once a bidder is the only small one remaining, he bids truthfully. Stopping early induces the remaining bidder to behave truthfully. Hence, each small bidder wants to be the first to stop bidding. The free-rider problem is considerably mitigated when there are many small bidders.     

Procurement auctions with ex-ante endogenous bribery

Corruption is a prevalent phenomenon in various procurement auctions. This paper explores a pattern of bribery between an auctioneer and a favored bidder, and also investigates the regulation scheme of buyer. In the model, the favored bidder is allowed to submit two bids simultaneously with the advantageous one to be announced; auctioneer decides the share of the difference between two bids which is the bribe transfer. The analysis shows that, the favored bidder does not participate in the corruption if his cost exceeds a threshold; otherwise he submits two bids whose difference is decreasing in the share. The corruption benefits both the auctioneer and the favored bidder but harms other bidders. The bribery endogenously leads to allocation inefficiency with a probability decreasing in the bribe share. Specifically, with two uniformly distributed bidders, we examine how the auctioneer optimizes the bribe share and how the buyer regulates the corruption. We find that, by driving the auctioneer to charge a higher bribe share that is less attractive for the favored bidder, severer regulation tends to reduce the probability of corruption. A buyer who adopts extremely severe regulation can exclude the corruption and achieve maximum social welfare, while a buyer who aims to maximize his own profit should tolerate some degree of the corruption.     

A Simple Model of Expert and Non-Expert Bidding in First-Price Auctions

This paper studies the equilibrium bidding behavior in a first-price sealed-bid auction when the number of informed bidders is not common knowledge. Both the independent private values and the common value cases are analyzed, under the assumption that a “neutral” signal exists. In equilibrium, experts and non-experts draw their bids from distinct supports: experts bid in the upper and lower tail of the bidding distribution and non-experts randomize their bids in between. For common values, it is shown that the seller's expected revenue always decreases with the probability of a bidder being informed when this probability is small. The opposite result is shown for the case of independent private values.Journal of Economic LiteratureClassification Numbers: D44, D82.     

Optimal collusion-proof auctions

We study an optimal collusion-proof auction in an environment where subsets of bidders may collude not just on their bids but also on their participation. Despite their ability to collude on participation, informational asymmetry facing the potential colluders can be exploited significantly to weaken their collusive power. The second-best auction — i.e., the optimal auction in a collusion-free environment — can be made collusion-proof, if at least one bidder is not collusive, or there are multiple bidding cartels, or the second-best outcome involves a non-trivial probability of the object not being sold. Regardless, optimal collusion-proof auction prescribes non-trivial exclusion of collusive bidders, i.e., a refusal to sell to any collusive bidder with positive probability.     

Sequential negotiations with costly information acquisition

Negotiations about a merger or acquisition are often sequential and only partially disclose to bidders information about each otherʼs bids. This paper explains the seller optimality of partial disclosure in a single-item private-value auction with two bidders. Each bidder can inspect the item at a nonprohibitive cost. If a revenue-maximizing seller cannot charge bidders for the information about the otherʼs bid, then the seller optimally runs a sequential second-price auction with a reserve price and a buy-now price. The seller prefers to keep the bids confidential and, sometimes, to hide the order in which he approaches the bidders.     

Auction fever: Rising revenue in second-price auction formats

The prevalent term “auction fever” visualizes that ascending auctions – inconsistent with theory – are likely to provoke higher bids than one-shot auctions. To explore and isolate causes of auction fever experimentally, we design four different strategy-proof auction formats and order these according to expected rising bids based on pseudo-endowment effect arguments (psychological ownership and disparity between willingness to pay and willingness to accept). Observed revenues in the experiment in the four formats rank as expected if bidders have private uncertain values (the private information of a bidder is the distribution of her value). A control treatment supports our view that the traditional private certain values approach prevents auction fever in the laboratory. Another control treatment with a procurement auction relates the auction fever bids to bids in a one-shot auction with real endowments. We conclude that, when bidders are uncertain about their valuations, auctions that foster pseudo-endowment may raise bids and revenues.     

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.     

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.     

Equilibria in second price auctions with participation costs

We investigate equilibria of sealed-bid second price auctions with bidder participation costs in the independent private values environment. We focus on equilibria in cutoff strategies (participate and bid the valuation iff it is greater than the cutoff), since if a bidder finds it optimal to participate, she cannot do better than bidding her valuation. When bidders are symmetric, concavity (strict convexity) of the cumulative distribution function from which the valuations are drawn is a sufficient condition for uniqueness (multiplicity) within this class. We also study a special case with asymmetric bidders and show that concavity/convexity plays a similar role.     

Bidding behavior and experience in internet auctions

We study the role of experience in internet art auctions by analyzing repeated bidding by the same bidder in a unique longitudinal field dataset. Our results show that experience significantly lowers the level of bids suggesting that bidders change their bidding behavior throughout time. Participating in more than ten auctions brings down average bids by up to 26%. We further test several possible explanations for the observed learning behavior and show that the change in bidding strategy is a result of a change in within-auction behavior that is generated with experience. Our results are robust to concerns of endogenous participation as well as bidder fixed effects.     

Strategic ignorance in a second-price auction

Suppose that bidders may publicly choose not to learn their values prior to a second-price auction with costly bidding. All equilibria with truthful bidding exhibit bidder ignorance when the number of bidders is sufficiently small. Ignorance considerations also affect the optimal reserve price.     

Commitment in sequential auctioning: advance listings and threshold prices

This paper models sequential auctioning of two perfect substitutes by a strategic seller, who learns about demand from the first-auction price. The seller holds the second auction only when the remaining demand is strong enough to cover her opportunity cost. Bidding in anticipation of such a contingent future auction is characterized, including a sufficient condition for existence of an invertible (increasing symmetric pure-strategy) bidding equilibrium that facilitates the seller’s learning. A unique invertible bidding equilibrium exists for the Dutch auction format, but only when the second auction is sufficiently discounted by the bidders. In the equilibrium, high-valuation bidders shade their bids down as if the second auction were guaranteed. To counter such strategic bidding, the seller would value ex-ante commitment to hold the second auction less often. Three forms of such commitment are analyzed: commitment to list future auctions in advance, commitment to not hold the second auction unless the first price exceeds a publicly announced threshold, and commitment to a reserve-price in the second auction. I would like to thank Georgios Katsenos, Thomas Jeitschko, Miguel Villas-Boas, George Deltas, and an anonymous referee for thorough and insightful feedback.     

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 insider's curse

The paper shows that in an open-ascending bid auction with multi-dimensional uncertainty about private and common value components, private information about the common value has negative value for a bidder if there are sufficiently many bidders. We discuss the role of the visibility of bids and the multi-dimensionality of private information for this result.     

eBay’s proxy bidding: A license to shill

We introduce a bidding strategy which allows the seller to extract the full surplus of the high bidder in eBay auctions. We call this a “Discover-and-Stop” bidding strategy and estimate that 1.39 percent of all bids in eBay auctions are placed by sellers (or accomplices) who execute this strategy. We argue that this kind of shill bidding is unnecessarily effective due to eBay’s proxy system and the predictability of other bidders’ bids. We also model eBay auctions with shill bidding and find that, in equilibrium, eBay’s profits are higher with shilling than without it. Finally, to determine whether bidders have an incentive to bid on their own items, we mimic the bidding behavior of shill bidders in actual eBay auctions and find some evidence of the strategy’s success.     

The value of an informed bidder in common value auctions

I compare two information structures in a common value first-price auction with two bidders: In one, each of the two bidders knows only his own signal about the value of the object, and in the other, one of the bidders learns his opponent's signal as well. Gaining the additional information in the second information structure makes the informed bidder worse off if the value is submodular in the bidders' signals and better off if it is supermodular. If the value is supermodular, then the seller's revenue tends to be lower with the informed bidder than without.