Factors that Distort Auctions — The Buy Side

In our first article in this series, we gave an overview of auctions, their history and the critical role they play in our economic and social infrastructure. We also highlighted the fact that not all auctions are conducted the same way, and explored some of the most common types of auctions. In this article, we’ll look at some of the factors that have led auctions to evolve into these divergent forms.

At their simplest, auctions offer a way for sellers and buyers to fairly and dynamically identify a price on which they mutually agree, without the complexity and time consumption of myriad individual negotiations. But while we’re most familiar with “English auctions,” which feature public bidding, escalating bids and first-price clearance (e.g., the winner of the auction pays the seller the amount that they bid), we’ve seen that there are many variants that alter one or more of these factors — implementing sealed private bids, bids that start high and decrease over time, or clearance of the auction at a price other than the first price.

These different auction forms have evolved as attempts to address factors that can distort outcomes in the standard auction model, leading buyers to make bids that differ from how they truly value an item — with the result that sellers get less revenue than expected — or causing buyers to pay more than they originally wanted, generating dissatisfaction with the auction.

In some cases, auction distortions may also be the result of purposeful collusion among buyers: For example, in December 2020, fast-food chain Chick-fil-A sued 17 top suppliers of chicken, arguing that instead of competing as individuals to win in the chain’s regular supplier bidding events, they shared bid details with one another, creating a de facto cartel in an effort to inflate poultry prices. (The prior month, one major supplier had pleaded guilty to conspiracy to limit competition and paid regulators a fine of $110.5 million, leading Chick-fil-A to expand its allegations to virtually the entire industry.)

And information-sharing cartels are just the tip of the bidder collusion iceberg: Bidders can engage in “auction pooling,” agreeing not to bid against one another in order to keep prices down for everyone. In 1987, the Department of Justice exposed auction pooling schemes taking place in bankruptcy auctions among 36 people and businesses across six states, impacting over $100 billion in auctioned goods sales. And bidders sometimes even align themselves in “bidding rings,” pre-allocating items being sold at auction among themselves, then bidding in such a way that the designated winners are guaranteed to get their respective items. Such rings are a constant risk in auctions that run on a frequent basis with a relatively fixed pool of regular buyers: In 2019, federal investigators busted a bidding ring in Mississippi that rigged millions of dollars in real estate foreclosure auctions, with nine people going to jail.

All of these are all examples of deliberate attempts to abuse and exploit auctions. But even without active manipulation, auctions can be distorted and made less efficient — producing less money for sellers, or reducing satisfaction for buyers — based on the impact of unintended social and psychological forces.

These distortions generally come about because one or more of the theoretical characteristics of fair and efficient auctions are not met under real-world circumstances. Auction designers face the challenge of creating auctions that are not just resilient to active manipulation, but also resistant to the volatile and discontinuous reality of their buyer and seller landscape.

Theory vs. Reality

In their landmark work around auction theory, R. Preston McAfee and John McMillan defined a generalized description of auctions that they called the “benchmark model,” which is rooted in four assumptions:

1. All of the bidders in an auction are risk-neutral.
2. Each bidder has a private valuation for the item that has been independently drawn from some probability distribution.
3. The bidders are being motivated by symmetric information and priorities.
4. Payment for the item being auctioned is represented as a function of only the bids.

When the assumptions of the benchmark model are met, they support an expectation of auctions called the “Revelation Principle,” which essentially states that well-structured auctions will incentivize bidders to report their valuation of an item honestly, rather than underbidding (“shading” their bids) or overbidding (and thus creating the buyer’s remorse phenomenon known as the “winner’s curse”).

Here’s an example of how an auction can give rise to “truthful” bidding. Consider the Japanese Auction format, in which the price of an item rises steadily higher, and participants hold a button down to signal if they wish to stay in the auction at each higher price. The auction ends when there is only one bidder left pressing their button; that bidder pays the price on the board at that time. In this context, truthful bidding — defined as continuing to bid until the price equals one’s actual valuation for the item being offered — is a dominant strategy, which is to say, a strategy that is always optimal, regardless of the strategies employed by other bidders.

To see this, we should note that the goal of bidders is to maximize their payoff. A winning bidder’s payoff is equal to their valuation of the item being auctioned, minus the price they paid for it. (For losing bidders, the payoff is automatically zero.)

If you’re participating in a Japanese auction, and your valuation for an item being auctioned is $50, your payoff is positive as long as the price you pay is lower than $50 (at a price of $30, for instance, your payoff is $50 — $30 = $20). If you bid and lose — by dropping out before the auction ends — your payoff is zero, the same as if you hadn’t bid at all. But as long as the price is below $50, submitting a bid gives you the chance of a positive payoff, while leaving you no worse off than not bidding. So for all prices below $50, it’s in your interest to keep pressing the button.

But as soon as the price exceeds $50, winning generates a negative payoff for you (for example, winning at a price of $60 produces a payoff of $-10, versus a payoff of zero if you drop out). As a result, it’s not in your interest to hold the button at those prices. As a result, the actions taken by other bidders don’t matter; it’s always in your interest to bid in accordance with your private valuation — i.e., to bid truthfully.

A fully optimized auction should produce a result where the auctioned item goes to the bidder with the highest valuation of the item, at a price equal to their true valuation of the item, while also delivering a price to the seller that meets at least their minimum expectations. When all four assumptions are met, each of the major categories of auction should deliver the same price result for the seller.

This result — known as the “Revenue Equivalence Theorem” — may seem surprising. But consider the case of our Japanese auction and a Vickrey (sealed-bid, second-price) auction for the same item. In the Japanese auction, each bidder will continue to bid until the price exceeds their valuation for the good; bidding stops when there is only one bidder remaining. Because the second-to-last bidder will drop out as soon as the price exceeds his or her valuation, the price paid by the winner will in fact be equal to the second-to-last bidder’s valuation. Similarly, in a Vickrey auction, it can be shown that the dominant strategy is again to bid one’s true valuation — and because, by definition, the winner of a Vickrey auction pays the second-highest price submitted, the winner will pay a sum equal to the valuation of the second-highest bidder, just as in the Japanese auction. While the argument for the revenue equivalence of other standard auction types is a bit more involved, it can be shown that, given the assumptions outlined above, sellers should be indifferent among them.

But of course, in the real world, the benchmark model’s assumptions are rarely met. Below are a few ways in which real-world conditions can deviate from these assumptions, and how those deviations produce outcomes that violate the predictions of the benchmark model.

Risk aversion

Risk-averse bidders are strongly motivated to reduce uncertainty, which affects their bidding strategy. This means in first-price sealed-bid and Dutch auctions, risk averse bidders will bid higher than they might otherwise; with only one chance to bid, they tend to overbid out of fear of losing the item.

This is not true of English and Vickrey auctions, however; in English auctions, risk-averse bidders receive constant information about what other bidders are willing to pay and can outbid them in real time, while in Vickrey auctions, risk-averse bidders pay the second price rather than their own bid, which may be from a bidder who isn’t as risk-averse.

Correlated values

In auction formats where bidders can obtain information about other bidders’ valuation of the item being auctioned, that information will shape their own perceived value of the item. One notable outcome of this is the “winner’s curse,” where the results of the auction convey to the winner that everyone else estimated the value of the item to be lower than they did, generating negative feelings on the part of the winner.

The impact of correlated values on an auction is reduced when there’s less information leakage between bidders. First-price sealed bid auctions have the least information leakage (since bidders only learn the winning bid price and in most but not all cases, the identity of the winner). Second-price sealed bid auctions allow bidders to know the price of the second-highest bidder (and winners know that price and their own bid). Open bid auctions allow information to be transmitted among bidders in real time, and result in the greatest degree of correlated values.

Bidder asymmetry

In the real world, potential buyers often have different information or priorities. This creates uncertainties that can often distort the outcomes of auctions. One way that auctioneers can reduce asymmetry of information is by providing as much data about the item being auctioned to bidders as possible, both positive and negative. If this data isn’t provided, the winning bidder may offset their maximum bid based on the estimated cost needed to acquire this information, or simply bid less due to uncertainty, leading to reduced revenue for the seller. By reducing discovery costs for all, sellers can boost the size of expected winning bids and encourage people to bid who might otherwise stay on the sidelines.

Additional payment requirements

In some auctions, the total cost of an item isn’t fully baked into the selling price alone — for example, auctions for items that require ongoing royalties or incentive payments, or that require other extraneous costs of production, supply or maintenance for the item that impact its true value. These additional payments end up getting factored into each bidder’s price function, and frequently in uneven fashion. To reduce the impact of this true-cost uncertainty, auctioneers may choose to make available any and all information that they have about projected extraneous costs, as well as to transparently disclose historical bid data — both of which can stimulate more competitive bidding.

All of these factors can be mitigated in different ways by auction design. But designing auctions to be resilient to active bidder collusion can be harder.

Detecting and Fighting Abuse

In fact, the best defense against bidder collusion often is simply early detection of patterns that can suggest unusual behavior, and awareness of the conditions that tend to encourage such abuse.

Some red flags that an auction platform may be experiencing bidder collusion include: The same players consistently winning or losing, or winning or losing in rotating fashion; early-round bids in auctions being significantly higher than expected; a much smaller than predicted number of competitors choosing to submit bids, relative to similar historical auctions; very big gaps existing between how a participant bids in different auctions for similar items; price outcomes from auctions being very similar or even identical for long periods of time; and items won in auctions being subsequently transferred to participants who lost the auction.

It’s also worth noting that bidder collusion is more likely to arise under certain conditions, including the following circumstances:

Constrained seller pool: If there are few sellers, buyers are more readily able to come together to share information or form auction pools or bidding rings. A very large seller pool makes buyer aggregation, and thus collusion, more difficult.

Restricted supply: Collusion is more likely to emerge when the items being sold are rare or have few substitutable alternatives, as the risk of getting zero wins outweighs the cost of sharing wins, incentivizing illicit cooperation among buyers.

Standardized item types: The more standardized a pool of items being auctioned is, the easier it is for competing buyers to come together to agree on how to divide the pool. Items that vary greatly in design, features, quality or rarity make this kind of coordination more difficult.

Frequent repeat auctions: Auctions for similar kinds of items that take place frequently are more likely to engender collusion, as a pool of regular bidders is more likely to emerge that is incentivized to collaborate, especially as social and other kinds of “insider” connections develop among them.

Localized auctions: Greater proximity among bidders tends to make collusion more likely, as it can facilitate real-time coordination and communication among collaborators. This proximity can be physical (e.g. bidders in geographic proximity) or virtual (e.g. bidders coming from a digitally connected in-group, such as belonging to the same chat group, guild or forum.)

Of course, good auction design can make collusion more difficult, because bidder collusion schemes tend to fall apart if their members can’t be prevented from breaching their cooperation agreements.

In non-repeating Dutch auctions and first-price sealed bid auctions, the “designated winner” is instructed to bid as close to the seller’s reserve price as possible while other colluders agree not to bid. But each of the colluding bidders could gain by simply placing a slightly higher bid than the designated winner in violation of the collusion agreement — there is no way for collusion to self-enforce in these types of auctions. (And honor among thieves is rare.)

But in English auctions and second-price sealed bid auctions, the “designated winner” is instructed to bid up to their own valuation, with everyone else not bidding or shading their bids (artificially bidding low). In these auction formats, no one gains by choosing to exceed the designated winner’s predetermined limit, allowing the collusion to be self-enforcing.

These are just some of the common ways that auction outcomes can become distorted based on the mindset or behavior of buyers. As we’ve noted, most of these issues can be mitigated by thoughtful auction design.

But buyers aren’t the only ones whose psychological states and behind-the-scenes actions can distort auction outcomes. Sellers are equally capable of altering auction outcomes in less than optimal ways as well — by directing wins to favored buyers, or engaging in activity that boosts the amount of revenue they receive in an exploitative fashion. The challenge, of course, is that auction designs that address buy-side distortions can make those on the sell-side worse.

In our next article, we’ll take a look at what those look like, and the complicated balance that auctions have to maintain between buy-side and sell-side concerns.

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