Bidding Strategies and Price Discovery

In our prior article, we looked at the challenges related to auction design in the context of real-world problems. In this post, we take a deeper dive into the price discovery function of auctions, and explore why classic auction formats don’t always guarantee the most desirable outcomes.

What is price discovery?

We usually don’t spend a lot of time thinking about how the prices we pay for many goods or services are determined. When we go to the grocery store, we simply look at price tags that have been marked by the store’s management and make a casual assessment of whether those prices feel cheap or expensive in contrast to other goods on the shelves, or our prior purchasing experiences. In economics terms, these are what’s called posted prices.

But prices can be determined in a number of ways. In housing markets, for example, where there’s significant bargaining over prices and other terms of sale, prices are determined in a back-and-forth negotiation between the seller and potential buyers.

Bargaining and posted prices are types of price discovery mechanisms: they’re methods by which sellers determine for how much and under what terms to sell a good or service. Like bargaining and posted prices, auctions offer another method of price discovery.

How do auctions facilitate price discovery?

As we’ve discussed, in a typical auction, potential buyers for an item submit bids in a pre-defined process. The auctioneer or auction manager selects the auction winner(s) and the price they pay based on the rules of the auction. The price that the auction winner pays depends both on the rules, and the composition of the participants in the auction.

Auctions are particularly useful for price discovery when the items being sold are novel or unique (for example, artworks), or when the most efficient allocations are impossible to determine in advance (radio spectrum), or when there are concerns about insider trading and collusion (bankruptcy fire sales).

The Revenue Equivalence Theorem

As we’ve discussed in previous articles, there are many different types of auctions. Does the type of auction used impact the amount that a seller can expect to earn?

An elegant result covered in every textbook about auction theory called the revenue equivalence theorem (RET) provides a reassuring starting point to consider when designing auctions. The revenue equivalence theorem states that under a specific set of economic conditions, the revenue an auctioneer can expect to earn and the profit any bidder can expect to make will be the same for a broad class of auctions.

In situations where the RET does apply, we can pick from a family of standard auction formats without worrying too much if there is another significantly better alternative. Unfortunately, this is far from the end of the story; there’s a lot more to consider as we unpack the conditions and assumptions required to obtain revenue equivalence.

How high is too high? Price discovery

For the RET to apply, the following conditions have to be satisfied:

  1. The seller has a single item to sell, with no prospect of resale
  2. The bidders are risk-neutral
  3. The bidders’ valuations of the item are independent of each other

The third and arguably most critical condition is called the private value model. It implies that a bidder’s value is idiosyncratic and would be unaffected by learning any other bidder’s information. For example, when bidding for things that are meant for consumption, like apparel or technological devices, people focus primarily on how much utility they personally might expect to derive from an item.

In contrast, in the common value model, everyone has the same valuation for an item, but different private information about what the value actually is. In this case, a bidder would change her estimate of the value if she learns what the other bidders are willing to pay. A classic example would be auctions for oil drilling rights. Bidders are concerned about the amount of reserve under an oil field. They each collect private information about the reserve by prospecting and assaying the field, and guard the information closely to protect their informational advantage.

Most practical auction settings involve a combination of private and common values, so the auctioneer will have to think about information aggregation and price discovery carefully. Price discovery is important for the bidder for obvious reasons. They want to have as accurate an estimate as possible to not overbid and purchase an item at a loss. They also want to be able to expect how much their competitors will bid, so they don’t lose an item for bidding too little. The seller also has an interest in facilitating price discovery. The more information bidders have about an object’s value, the higher the revenue and the more likely the item will go to the person who values it the most (efficient allocation).

Bidding strategies that achieve equilibrium

Different auction designs can yield different outcomes. Their effectiveness in price discovery is in part shaped by their impact on buyers’ bidding strategies.

Truthful bidding, where bidders submit bids equal to their actual valuation, is a desirable way to achieve an equilibrium in bidding strategies — that is, a situation where each bidder would not do better in the auction by changing their bid. That’s because when all bidders bid truthfully, the barrier to enter an auction is minimal. Anyone can figure out their individually optimal bid without gathering additional information or second-guessing what other bidders will do. It also makes it easier for the seller to design an auction and calculate the revenue. Theory predicts that we can expect truthful bidding to prevail in private value second-price auctions, and observations in the real world tend to support such a prediction.

However, in many other auction settings, in equilibrium, bidders would want to bid less than their own valuation (shading). Outside of the safe space of the RET, shading can be accompanied by a problematic phenomenon called the winner’s curse. Specifically, if different bidders have different information about the same common value, then the person who overestimates it the most will become the winner. The winner gets stuck paying more than the actual worth of the item. Bidders wary of the winner’s curse will shade their bids even more, which in turn reduces the expected revenue of the auction.

How information is revealed to bidders over time and how price discovery is integrated into the bidding process is crucial in determining the size of the winner’s curse. English auctions, where publicly observable bidding starts low and prices go up, are better than Dutch auctions, where bidding starts high and prices go down, at mitigating the winner’s curse. This is because bidders gain more information about an item’s value during the bidding process as they observe their competitors. It is helpful for bidders to know both what other bidders do and what they choose not to do. In a Dutch auction, bidders can only infer that no one’s valuation is higher than the current asking prices; in an English auction, bidders can make more precise inferences about the valuations of those who made bids and also those who dropped out.

There is another hurdle to applying theoretical predictions of bidder strategies to real-world auction design. The degree to which bidders adhere to the mathematically optimal bidding strategies varies depending on the complexity of the calculations required to determine reasonable bids. As hinted above, truthful bidding requires very little input when it is an equilibrium strategy. On the other hand, an optimally shaded bid will have to take account of a best-value estimate based on the best available information; how other bidders evaluate the item based on different sets of information; and the probability of winning the auction with any given bid — a much more complicated calculation. Most times, bidders resort to past experiences and heuristics. The deviations caused by these attempts at strategic bidding can be small on an individual level but economically significant for the final outcome.

It’s therefore important to combine the predictions of any theoretical models with real-world examples and experiments that shed light on the behavioral tendencies of bidders.

Tailored Solutions to Balance Conflicting Objectives

Often, given difficult tradeoffs between conflicting objectives, the right auction format depends crucially on the nature of the item(s) being sold and the priorities of the auctioneer.

Sotheby’s art sales follow a time-honored tradition of English auctions, which put a strong emphasis on transparency and real-time price discovery. Most artworks are unique and require a special set of expertise to evaluate properly. Having the bids submitted publicly, and in many cases, the identity of the bidders observable, English auctions prevent an expert with exclusive knowledge from buying valuable artworks at a big discount and help increase the auction house’s revenue.

Flowers in the Netherlands are sold through Dutch auctions. Bidders have only a few seconds to bid on the flowers before they are sold and passed on to the new owner. The format makes sense because flowers are easily perishable and relatively standardized. Flowers at sale through Royal FloraHolland are subjected to many quality checks so that they can be graded on a scale.

Another fascinating example is the paradigm shift in the marketplace for online advertisement slots. Ever since the birth of programmatic advertising, auctions have been used to help the buy and sell-side to value inventory properly. For a long time, generalized second-price auctions where the winner pays $0.01 more than the second-highest bid were the most prevalent format. In 2019, the dominant player in the market, Google Ad Manager, switched to first-price auctions where the winner pays exactly the price they bid on the advertising impression. The change was introduced despite second-price auctions’ well-known virtues, because an FPA enables more transparent bidding and more accurate evaluation of inventory value, and, as we’ve noted, avoids the perception (and perhaps the reality) of auction rigging by ad sellers, who might engineer fake second-price bids to boost the prices they receive.

Of course, auctions aren’t always the best way to achieve price discovery. We’ll discuss when auctions should be implemented, and when other transaction mechanisms offer advantages, in our next post.

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