Procedural Explanations for Overbidding

Although little research has directly addressed why people overbid in Vickrey auctions, Kagel, Harstad, and Levin posit a procedural explanation. The Vickrey mechanism itself is not transparent because bidders cannot directly see the tradeoffs of their actions at the time they place their bid. Bidders might consider that there is no direct cost to increasing their bid, because they will never be called upon to pay the bid price—only the second-highest bid price—should they win. If they treat the second-highest bid price as fixed and below their valuation, they will not recognize any cost to increasing their bid. On the other hand, increasing their bid increases their chance of winning the auction. Without recognizing the cost of increasing their bid, they overvalue their ability to win. Unfortunately, the only auctions that may be won by bidding above one’s valuation and that cannot be won by bidding one’s valuation are auctions you don’t want to win. In any case where it is necessary to bid above your valuation to win, you lose value by winning the auction. One useful way to think about this behavior is as a result of anchoring and adjusting. Just as in the case where bidders created a willingness to pay for items based on an arbitrary anchor, now bidders are forming bids based on an anchor. In this case, bidders anchor on the private valuation they are given. Then, falsely believing they can increase their bid from the anchor without penalty, they adjust upward, a procedure that is likely to make a loser of the highest bidder.

EXAMPLE 5.2 Timing of Bids and Online Auctions

The online auction site eBay employs a second-price auction, but the current price (or current second-highest bid) is always visible throughout the duration of the auction. Participants are able to revise their bids at any time before the auction closes, yet at the time specified for the end of the auction, all bids are final. Amazon.com offers a very similar auction mechanism. The primary difference is that whereas there is a specified time for the bidding to end, if a bid is placed in the last 10 minutes, an additional 10 minutes is given for bidding. This addition of time can happen several times. Thus, the auction does not end until the time for regular bidding has elapsed and at least 10 minutes has passed without an additional bid. Amazon introduced this feature to eliminate the prevalence of sniping. Sniping occurs when a bidder observes bidding behavior by others and then at the last minute places a bid in an attempt to prevent others from responding to that bid. Online sites offer software that is specifically designed to allow sniping in eBay auctions.

If all bidders understood the rules of the game and knew their certain private valuation of the object, their dominant strategy would be to bid their value and wait for the end of the auction. If a last-minute bid exceeded their own, they should be happy to lose to ensure they do not spend more than their valuation. However, this is not what is observed. Rather, Alvin Roth and Axel Ockenfels found rapid run-ups in bidding in the final moments of auctions on eBay, suggesting a sniping strategy is employed by many users. Alternatively, the auctions on Amazon.com more nearly represent the laid-back, once-and-for-all bidding behavior commonly modeled by economists. If rationality suggests once-and-for-all bidding that is independent of the behavior of others, why should anyone care about sniping?

Levels of Rationality

There are several reasons why people engage in sniping. If all others are following the strategy of bidding their value once and for all, then it is rational to bid your valuation once and for all as well. This would constitute a Nash equilibrium. But suppose others did not follow the Nash equilibrium strategy. For example, suppose you knew there were others who would engage in bidding wars by always bidding just a little bit higher if your bid exceeds theirs. Then, bidding your value early in the game will ensure that they bid higher and take the auction with no possibility of benefit for you. Alternatively, if you waited for the last instant to place your bid and bid your value, they might have no time to respond and you could obtain the item with a potential net gain.

Another possibility is that others might mistakenly ignore the auction mechanism and believe that this is a sequential first-price auction. Suppose some players naïvely bid below their valuation, waiting for higher bids from competitors before increasing their bid. We call this incremental bidding behavior. In this case, it is again optimal to put off bidding until the last minute so that other bidders do not have the chance to respond. By doing so, the second-highest bid is minimized and bidders can maximize their net benefits from having won the auction.

Finally, people might increase their attachment to the item through the process of bidding on the object. For example, bidders might begin to incorporate the item in their reference point and thereby increase their valuation via the endowment effect, leading to higher bids toward the end of the auction. For example, if they know they have the highest bid for a time, they might begin to regard the item as theirs and increase their valuation. Then when the bids increase above their prior bid, they now feel they need to bid higher.

A follow-up study by Dan Ariely, Axel Ockenfels, and Alvin Roth used an experimental setting to determine the reasons behind sniping behavior. Essentially, they had participants engage in experimental auctions designed to mimic the properties of the eBay and Amazon auctions, except that bidding took place in well-defined bidding periods, and the object of the auctions were induced values. Induced values means each participant was randomly assigned a value for winning the auction, as in the other experiments described previously. They found some evidence that bidders engage in sniping behavior as a rational response to incremental bidding by others. This creates an interesting situation whereby people might respond rationally to behavior that appears to be less than rational. This has led to a literature hypothesizing several different types of players who differ in their level of sophistication or rationality.

For example, Dale Stahl and Paul Wilson posit one type of player that does not think strategically at all, rather just randomly choosing actions with equal probabilities assigned to each. A second type (which may be thought of as a first-level rational model) thinks about their own payoffs, considering that all others simply choose their actions at random; in other words, this type believes they are the only strategic players. One can imagine further types who consider the mix of strategic and nonstrategic players and formulates a strategy based on the anticipated behaviors. Thus, in games, we must differentiate between irrational behavior and behavior that is rationally motivated by the irrational behavior of others.

EXAMPLE 5.3 English Auctions and Magic

In an English auction, an auctioneer calls out an initial price. All those willing to pay this price indicate their willingness to buy at the initial price. Then the auctioneer raises the price by some small increment. At each increment, bidders must again indicate that they are willing to purchase at that price. The auction ends when there is only one bidder who is still willing to purchase. Variants on the English auction are used to sell rare antiques at large auction houses. The English auction can be called a first-price open-bid auction because the highest bid wins, and all are aware of all other bids at all times. The dominant strategy in this case would be for a bidder to continue to indicate willingness to purchase until the price is raised above his or her valuation of the good. Because the auction stops when only one bidder is left, the price is exactly one increment above the second-highest bidder’s valuation of the item. Thus, the English and Vickrey auctions should produce the same result both in terms of price and winner.

David Lucking-Reiley used a field experiment to test the equivalence of these two auctions. He auctioned off sets of trading cards that are part of the role-playing game Magic: The Gathering. In the game, each card represents a spell that can be cast, providing the owner with a more interesting gaming experience. Lucking-Reiley auctioned off 184 of the trading cards using a Vickrey auction, and he auctioned off another 184 cards using an English auction. Participants were solicited in online chat communities that regularly trade and auction these cards. Hence, one might consider these to be experienced traders. The cards used for the auctions were selected to have a similar value and quality. The results were somewhat mixed. In an auction with a large number of bidders, the Vickrey auction bids were substantially higher than the English auction bids. However, there was some evidence that the relationship was reversed with a smaller number of bidders.

Previous laboratory experiments using randomly assigned individual values by Kagel, Harstad, and Levin found that Vickrey auction bids were predictably and regularly higher than English auction bids. Whereas the Vickrey auction bids were persistently above valuation, the majority of English auction bids were below valuation, though by a very small amount. Further, participants in the English auction appeared to adjust their strategy after each session, eventually converging on bidding their valuation. Thus, experience with the English auction mechanism tended to lead bidders to eventually recognize and use their dominant strategy.

Bidding Heuristics and Transparency

Why the potential difference between Vickrey and English bidding? Previously, we reasoned that in the Vickrey auction, people anchored on their value and then adjusted up for the apparent gain in probability of winning without apparent cost. In the English auction, the price is transparent. This means that at the time of bidding, the bidder knows what the price will be if his bid wins. Further, the English mechanism draws full

attention to this price. Thus, little reasoning effort is required in the English auction for bidders to determine their dominant strategy. If the price exceeds their value, they won’t bid. Determining the dominant strategy in the Vickrey auction can require some significant level of cognitive effort, leading bidders to give up on determining the optimal bid in favor of a rule of thumb such as that suggested by anchoring and adjusting. The transparency of the English mechanism not only facilitates reasoning out the dominant strategy bid, it also facilitates learning over time. Even if one had a difficult time discerning one’s optimal bid in the first few rounds of an English auction, after watching the announced price rise, seeing the final bidder still standing, and then seeing the announced price, it would be difficult to persist in the notion that one should bid above their valuation of the object.

Although people have a strong tendency to overbid in Vickrey auctions, they display a somewhat weaker tendency to underbid in the English auction. This deserves some additional analysis. In the Vickrey auction, people appear to anchor on their valuation and adjust upward. In the Vickrey auctions conducted in the laboratory, bidders are given no numbers to anchor on except their randomly assigned valuation. As was seen in the previous chapter, having any number presented in the process of eliciting a willingness to pay from the participants can influence the final bids. Without anything else to anchor on, the randomly assigned valuation becomes the anchor for bidding. In the English auction, the bidding process invariably starts with a minimum bid and slowly works its way up until the final bidder is the only one left. This initial bid might serve as an anchor to those who, for whatever reason, do not take advantage of the transparency to determine the dominant strategy bid. Thus, those who use this initial bid as an anchor will adjust upward toward their optimal bid but not quite reach the dominant strategy bid, leading to nominal underbidding behavior. In fact, Patrick Bajari and Ali Hortaçsu found that increasing the minimum bid increases the revenue for rare coins auctioned on eBay, using their second-price auction mechanism. This suggests that minimum bid levels can influence the bidding behavior in Vickrey and English auctions.

Finally, the lack of clear evidence of higher bids in the Vickrey auction for Magic cards deserves some mention. The Vickrey auction has produced clearly higher bidding than the English auction in dozens of published laboratory experiments. The result in the online field experiment calls these results into question. However, this experiment was conducted in a very experienced community and one with an active trading market for all cards involved. It could be that such a market context draws only bidders who have substantial experience with auctions and bid formation. The laboratory experiments show no evidence of improved bidding behavior with experience, but the laboratory presents a very special sample. Over the course of obtaining experience, no bidders are allowed to drop out of the auctions in the laboratory. On the other hand, public auctions such as those conducted for Magic cards might draw only those who prefer to obtain their cards through an auction. Those who have gotten burned by an auction in the past might simply drop out and never bid in an auction again. Thus, whereas a bidder might display no particular effects of learning in a Vickrey auction, experienced bidders might behave more like the dominant strategy because poor bidders are weeded out of the market.