How to win an auction without losing

"I'm ready to pay 6,000 dollars for the car. So I bid up to 6,000?"

Anna is buying a car at IAA's online damaged-car auction in Canada, so all amounts here are in Canadian dollars. $6,000 is everything she's ready to hand the auction. But the bid is only the hammer price. On top, the buyer pays fees, and the biggest of them, the buyer fee, rises in steps with the price. There's also a pull-out fee, an online bidding fee and a 1% digital fee ($5 to $50).

The fees are no trifle: 16% of the bid. And they rise in steps: once the bid passes $5,500 the buyer fee jumps, and from $6,000 the online fee goes up too. So the limit is worked back from the full amount to the bid, before the start, not during the bidding. On other platforms the numbers differ, but the principle is the same: auction houses charge a buyer's premium, and eBay and ad systems have their own fees and taxes.

• Bid limit = what you're ready to pay in all minus every fee, shipping and tax.
• Work it out before the start, from the platform's fee table: there's no time during the bidding.

This builds on what you haven't done yet: chapter 1, “What the lot costs you”

"I spent three days choosing this car and paid for an inspection. Am I really going to give it up over a mere 200 dollars?"

Anna set her limit in advance (chapter 1). Before the auction she paid $150 for an inspection and a vehicle history report. The live auction is on, and two bidders are left: her and one other buyer. The bid is already $200 above her limit, with a few seconds to go.

Money you can't get back is called a sunk cost. It weighs on anyone who has waited a long time for something, and at an auction it weighs double: the rival thinks the same way. Each next step seems small ("another $100 and it's mine"), but together the steps add up to a sum neither of the two meant to pay. Bidding where both are long past their limits and neither gives in is called escalation.

• Write your limit down before the auction and don't revise it during: new information about the lot is a reason, excitement and "I've put so much in" are not.
• Costs that stay whatever the outcome don't affect how much to bid.
• Proxy bidding with a limit (chapter 4) protects you from yourself: in the last seconds the decision is already made.

"I won a lot that nine others bid on too. That's good, right?"

Anna's next car is a flood car. Nobody knows exactly what the repair will cost, but it's the same for every buyer: once repaired, the car is worth $10,000 to any of them. Each looks at the photos and the report and estimates its value with an error of up to $2,000 either way: some higher, some lower, with no systematic bias. Proxy bidding makes the auction second-price: the winner pays the estimate of the bidder just below (chapter 4).

The more bidders, the surer it is that one of them has badly overestimated the lot, and the surer it is that this one wins. So winning is news in itself: "everyone else valued the lot below me". Experienced buyers take that news into account before bidding and shade their estimate more, the more rivals there are. With 10 bidders in this example, breaking even would mean lowering the estimate by about $1,300.

• The winner's curse works where the lot is worth roughly the same to everyone, but its value is known only roughly: damaged cars, land, licences, tenders (chapter 11).
• The more bidders, the more you should shade your estimate before bidding.
• If the lot's value is purely personal (you just like that colour), the curse weakens: then the limit from chapter 1 decides.

"I'll bid a bit less than I'm willing to pay. Maybe it'll come out cheaper?"

Anna is looking for a camera lens on eBay. It's worth $100 to her. Such lenses sell for anything from $50 to $150, so the maximum of her one serious rival can be anywhere in that range. eBay uses automatic bidding: you enter the highest price you're willing to pay, and eBay raises the bid for you in minimum steps, but never above your limit. So the winner pays roughly the rival's maximum plus one step.

Proxy bidding turns open bidding into a second-price auction: the highest maximum wins and pays the next one. In such an auction an honest maximum is best whatever the rivals do. Your bid only decides whether you win; what you pay is decided by others. So "how much should I bid" comes down to "what is the lot worth to me", which chapter 1 answers.

• An auction with proxy bidding (eBay, live car auctions with a preliminary bid): enter your true limit, no less and no more.
• A maximum below your value saves nothing; it only loses profitable lots.

• Expected value

  The average result you can expect if you repeat the same thing very many times.

This builds on what you haven't done yet: chapter 4, “Automatic bidding on eBay: bid your limit”

"If proxy bidding bids for me anyway, why do people wait for the last seconds?"

The same lens, Anna's limit $100. This time the rival behaves differently: he'd pay up to $120, but doesn't enter it all at once. He started at $52 and adds $10 every time he's outbid. Let the bid step be $1: on eBay it depends on the lot's price.

Roth and Ockenfels compared eBay, where an auction ends at a time fixed in advance, with Amazon's auctions of those years, where every late bid pushed the end back. On eBay the last bid came in the final 5 minutes in 40% of computer auctions and 59% of antiques auctions, on Amazon in about 3%. And experienced eBay buyers bid later than novices, while on Amazon they bid earlier. Sniping isn't a trick of a few people; it's a response to the ending rule.

The rules change. eBay has added "extended bidding": any bid in the last 60 seconds resets the clock to 60 seconds. In Australia all auctions have ended this way since 17 August 2026, and in the UK the rule is being tested in some categories. Before planning a late bid, check the ending rules on the lot page.

• A hard end: a late bid can save money, because it gives no time to those who raise step by step. But still bid your limit, no more.
• An extending end: sniping is pointless, enter your limit as a proxy bid (chapter 4).
• Don't raise step by step yourself: that's how you set the price up for whoever waits for the last seconds.

This builds on what you haven't done yet: chapter 4, “Automatic bidding on eBay: bid your limit”

"Here everyone submits one bid in an envelope, and the winner pays their own. Should I write it honestly?"

A company is selling off its vans by sealed envelopes: the highest bid wins and pays what it wrote. That's a first-price auction. To each buyer a van is worth between $0 and $10,000, any amount equally likely, and to Anna it's worth $8,000. There is one rival, and he's sensible too.

With more rivals a low bid loses more often, and the best share grows: with one rival it's half the value, with three it's three quarters, with nine it's nine tenths. The general rule for such an example: (n − 1)/n of your value, where n is all the bidders including you. But never write your full value: then winning gains you nothing.

• First price (envelopes, the winner pays their own bid): write less than your value, and the closer to it, the more rivals there are.
• The best bid depends on how the others bid. Here they're sensible; how to guess how many steps others think ahead is shown by the problem below.

This builds on what you haven't done yet: chapter 4, “Automatic bidding on eBay: bid your limit”chapter 6, “A sealed envelope: shade your bid at first price”

"I'm selling an old camera. Should I set a hidden minimum price? What if then nobody buys?"

Now Anna is selling. The camera just sits around, so it's worth nothing to her. There are two buyers, and to each it's worth between $0 and $100, any amount equally likely. It's an auction with proxy bidding, so the buyers bid honestly (chapter 4). On eBay a seller can set a reserve price: it's hidden, and buyers only see whether it has been met. If not, the lot isn't sold.

A reserve is the seller's own bid: it becomes one more "bidder" and lifts the price when there's no real competition. It helps most when there are few buyers. With four buyers the same $50 reserve raises revenue only from $60 to $61.25: the competitors already hold the price up. And extra buyers beat any reserve: from two to four buyers revenue rises from $33 to $60.

• Selling with few buyers: set a reserve, even if the lot sometimes goes unsold.
• The seller's biggest lever is the number of buyers: photos, a description, a good ending time.
• Buying: "reserve not met" means the seller values the lot above the current bid. Don't stretch your limit to meet it.

• Variance and standard deviation

  A measure of spread: how far values typically stray from the mean. The standard deviation is its square root, in the same units.

This builds on what you haven't done yet: chapter 6, “A sealed envelope: shade your bid at first price”

"The price drops every second. Press "Stop" as soon as it reaches my price, or wait?"

In a Dutch auction the price doesn't rise, it falls: a clock lowers it step by step, and the first to press "Stop" buys the lot at the current price. The format takes its name from the flower auctions in the Netherlands, and it is also used, for example, by Ukraine's state sales platform Prozorro.Sale: the price falls from 100% of the starting price in 1% steps, and the first to stop the fall fixes the price. A short round of sealed bids follows there, but the key decision is when to press.

There are four bidders. To each the lot is worth between 0 and 100% of the starting price, and to Anna 80%.

• A Dutch auction is a first price with a clock: decide in advance at what share of your value to press, and don't wait longer.
• The clock gives no new information: until someone presses, you only know that everyone is waiting.

This builds on what you haven't done yet: chapter 4, “Automatic bidding on eBay: bid your limit”

"I want my shop to be first in search results. Should I raise my bid to the max?"

When someone searches on Google, the ad slots above the results are auctioned. A slot isn't decided by the bid alone: Google computes an Ad Rank from six factors, among them the bid, the quality of the ad and the landing page, thresholds and the search context. And you pay, in Google's words, only what's minimally needed to clear the thresholds and beat the next advertiser. So it's an auction like the second price, but for several slots at once.

A simplified example where all ads are equally good. There are two slots: the top one gets 200 clicks a day, the second 199. There are three advertisers: a click is worth $10 to Anna and $4 and $2 to the other two. Each pays per click the bid of the one just below. The rivals bid honestly, their value of a click.

So in such an auction (called the generalised second price) an honest bid isn't always best, unlike chapter 4. Edelman, Ostrovsky and Schwarz showed in 2007 that honest bids aren't an equilibrium here, and advertisers really do bargain over the price of an extra click. And the 2024 court ruling in the US case against Google described the search ad auction as a "classic second-price auction, with modifications", among them "pricing knobs" with which Google tunes what advertisers pay.

• Don't ask "which slot", ask "what does an extra click cost" in the higher slot, and compare it with what a click brings you.
• The quality of the ad and the page is part of the rank: a better ad takes the same slot for a lower bid.
• Check which ad is better with a test, not by eye: how to find the best of several quickly is shown by the problem below.

"A competitor bids twice as much as I do. Do I even stand a chance?"

On Facebook and Instagram each impression is auctioned too. According to Meta, the ad with the highest "total value" wins, and that's made up of three factors: the bid, an estimate of how likely the person is to take the desired action, and the ad's quality. Meta doesn't publish exactly how it combines them, so the example below only illustrates the idea: we multiply the bid by the action rate.

The competitor bids $10 per purchase, and his ad gets a purchase in 1% of impressions. Anna bids $4, and her ad gets a purchase in 3% of impressions.

• In ads the highest expected value of an impression wins, not the highest bid. A better creative and a sharper audience are often cheaper than a higher bid.
• Meta promises its adjustments won't make you pay more than your bid. And a bid cap is a limit, not a price: your reports will show a different, usually lower, amount.

This builds on what you haven't done yet: chapter 3, “The winner's curse”chapter 6, “A sealed envelope: shade your bid at first price”

"The airline asks how much it would take for me to fly later. How much should I ask?"

Airlines sell a few more tickets than seats, because some people don't show up. When everyone does, someone has to stay behind. In 1968 the economist Julian Simon proposed not to bump people at random but to hold an auction: volunteers write how much they want for a later flight, and those asking least get the money. The US regulator allowed this in 1978. According to press reports, Delta collects such bids already at online check-in and at kiosks, and accepts the lower ones first.

Anna doesn't mind flying later if she gets $200 (a voucher for future flights). One volunteer is needed, and there are five candidates including her. Every other one's minimum is any amount from $100 to $600, and they also ask sensibly.

The airline's ceiling is the compensation it would have to pay a passenger bumped involuntarily. In the US since 22 January 2025 that's 200% of the one-way fare, capped at $1,075, if a domestic flight arrives 1–2 hours later, and 400%, capped at $2,150, if later than that. So asking more is pointless: bumping someone would be cheaper. And in 2017, after the scandal of a passenger dragged off a United flight, Delta, according to press reports, let supervisors offer volunteers up to $9,950 instead of $1,350.

A tender: the winner's curse in reverse

Anna, as a supplier, bids on a public tender: the buyer takes the cheapest offer. That's a reverse auction too, and the winner's curse from chapter 3 lives in it, only inside out. The cost of the job is the same for everyone, but each estimates it with an error, and the lowest price comes from whoever underestimated it most. So a won tender is a reason to recount your costs.

In Ukraine this is how Prozorro, the fully open public procurement system where every tender can be seen online, works. Its auction runs in three real-time rounds, bidders see each other only as "Bidder 1, 2…", and whoever offered the lowest price moves last in a round. There are guards against the winner's curse: a price far below the others' must be explained within one working day, and a winner who refuses to sign the contract loses the tender security. So a price that's too low costs money even if you spot the mistake in time.

• A reverse auction where you're paid your own ask: ask more than your minimum, but the closer to it, the more competitors there are.
• Know the buyer's ceiling: on an overbooked flight it's the compensation for involuntary bumping.
• A tender: build in a margin for cost errors, the larger the more bidders there are.

"Camera bags show up every day, and each is gone within a day. Take the first decent one or wait for a better one?"

On eBay an auction lot can have a "Buy It Now" button, but it disappears after the first bid, and the lot carries on as an ordinary auction. Anna wants to buy a bag as cheaply as possible. Over 10 days 10 "Buy It Now" offers will appear, one a day, with prices in random order. She must decide on each at once: the next day it's gone. All she has are the prices she's already seen.

• When offers come one at a time and vanish, first look at some of them without buying, to learn the price level, then take the first one better than everything you've seen.
• An auction with "Buy It Now": if the "now" price is below your limit (chapter 1) and similar lots rarely end cheaper, take it before the first bid, as the button won't be there later.

One question from each chapter. Go through them before you press "Place bid".

How these ideas work in puzzles without money is shown by the catalogue's "Games" problems: four auctions, the dollar auction and guess 2/3 of the average.