You’re at a blind auction, and the rules are simple. If you see something that you want, place a secret bid, and the item will sell to the highest bidder at their stated price. You would love to take home that new laptop or concert ticket or dinner with a local celebrity, but how much should you bid? Even if you can perfectly quantify what each item is worth to you, you still face a dilemma: You have no idea how others will bid. Should you bid close to your personal maximum and risk overpaying if everybody else bids low? Or should you bid low yourself and hope to get lucky? A clever yet simple tweak to the rules of the auction eliminates this strategic guessing game and replaces it with an incentive rarely found in money games: honesty. The tweak has inspired real-world auctions that power e-commerce and helped earn its inventor a Nobel Prize in economics.
The branch of economics known as auction theory calls the scenario above a first-price sealed-bid auction. Sealed-bid means bids are private, and first-price indicates the winner pays the highest price among all of the bids. In 1961 Columbia University professor of economics William Vickrey proposed an ingenious alternative. In his version, the highest bidder still wins but only pays the amount of the second-highest bid.
This peculiar twist has a radical effect on the bidders’ incentives. In a first-price sealed-bid auction, bidders are incentivized to shade their bids—that is, to offer less than what they consider the object’s true value to avoid overpaying. But in a second-price sealed-bid auction (also called a Vickrey auction) the best move would be to bid an amount equivalent to the object’s worth to you. No game-playing is required.
On supporting science journalism
If you’re enjoying this article, consider supporting our award-winning journalism by subscribing. By purchasing a subscription you are helping to ensure the future of impactful stories about the discoveries and ideas shaping our world today.
Suppose you’d pay at most $100 for a concert ticket. In the first-price auction, it never makes sense to bid more than $100, because even if you won the ticket, you would, in effect, lose money by paying more for it than it’s worth to you. Bidding exactly $100 doesn’t help because at best you break even. The ideal bid is the smallest one under $100 that still wins. If you knew the next-highest bid would be $70, then bidding $70.01 would win you the ticket and net you $29.99 of value. Unfortunately this strategy requires predicting the behavior of others, which is difficult in practice.
Why does the second-price auction incentivize honesty? You might feel tempted to bid a lot, say $500, to secure a win while only paying the second-highest bid. Somebody else, though, may have the same bright idea, leaving you on the hook to pay way more than your value for the ticket. If this doesn’t happen, and the second-highest bid is under $100, then you could have achieved the same outcome by bidding honestly at $100 without the risk. You also shouldn’t underbid. If you win, then you would have won anyway with an honest bid (and paid the same amount). But if you lose to a bid of less than $100, then you miss out on a deal you would have gladly taken.
Vickrey auctions not only reward honesty but also ensure that the item goes to the person who values it most (assuming everybody plays rationally). First-price auctions lack this guarantee because strategic underbidding with incomplete information about other players may result in someone with a lower valuation winning.
Both of the auction types discussed so far involve quietly sealing a single bid in an envelope. But when many of us picture an auction, we imagine the so-called English auction where a speed-talking, gavel-wielding auctioneer shouts increasing prices as bidders raise paddles to vie for the prize. When you hear “Going once, going twice— sold!” the last person who raised their paddle wins the item at whatever price they bid. The less common, though equally intriguing, “Dutch auction” flips the concept. Here the auctioneer begins with a sky-high price that nobody would pay and gradually lowers it until one person jumps in to buy on the spot.
Although the real-time, dynamic nature of English and Dutch auctions make them appear unrelated to the sealed-bid models, an unexpected correspondence unites them. Recall that the sealed-bid auctions elicited different strategies from buyers depending on whether they expected to pay the highest bid amount (in which case they should predict the highest competing bid and offer a hair above it) or the second-highest (in which case they should bid their honest value for the item). Amazingly, English and Dutch auctions incentivize these same strategies. Care to guess which one maps to which?
In a Dutch auction (where the price descends), you don’t want to stop the descent right at your honest value, because you would pay your maximum. Instead you want to predict the highest bid that’s not yours and cut in just above it—exactly the same thought process as a first-price sealed-bid auction. English auctions (where the price ascends), on the other hand, incentivize honesty. You’re willing to pay every new price up until your true value for the item, at which point you drop out. The winner in an English auction essentially pays the second-highest bidder’s stopping point, much like in a second-price sealed-bid auction.
The similarities among the four auction types run even deeper. So far we’ve focused on buyer strategies but have neglected the seller’s perspective. Which auction should a seller conduct to make the most money? Here comes another surprising twist from auction theory: they’re all equivalent. The revenue equivalence theorem states that, under certain idealized mathematical conditions, a seller should expect the same revenue under all four auction types. The specific assumptions are too in the weeds to list here, but they include things such as rational bidders who are neither risk-averse nor risk-loving and who know some information about how the other players arrive at their valuations.
Why do researchers study four types of auctions if they all yield the same financial outcome? It turns out the key differences are less about theory and more about practical considerations. For example, Dutch auctions work best for perishable items because they resolve quickly—only one person ever needs to bid for a sale. For instance, Royal FloraHolland hosts the largest flower auction in the world. Every weekday Dutch-style auction clocks tick down prices for floriculture products, and the first bidder takes them home at that moment’s price.
We’ve assumed so far that buyers know their personal valuation of the item for sale. But what if nobody, including the seller, knows its true worth? In these contexts, English auctions prove especially useful, because their open, incremental bidding reveals information about others’ valuations. This dynamic helps explain their popularity for rare goods like art.
While Vickrey auctions, in their purest form, haven’t proliferated (except in stamp auctions, where their dominance dates back to the late 1800s), the second-price concept has inspired hybrid models in widespread use today. The most notable example is eBay. A potential buyer privately tells the site their maximum bid, and then eBay automatically increases their offer just enough to outbid competitors, up to that maximum. The winner pays slightly more than the second-highest bid.
Researchers continue to study questions about the real-world implications of different auction designs: Which ones elicit the most fiscally rational behavior in practice? Which types resist harmful collusion? And which systems feel the best to win or the worst to lose? Vickrey won an economics Nobel in 1996 in part for his contributions to auction theory. He stands out among laureates as the man who proved that sometimes honesty is the best policy.
