An All-Pay Auction

Martin Shubik invented a famous game-theory exercise, sometimes called “the dollar auction,” where a teacher auctions off a $20 bill to the highest bidder. Bids have to be in round dollar amounts, but the twist is that both the highest and the second-highest bidder have to pay. When uninitiated students start to play this game, someone rushes to bid $3 or $4 dollars for the prospect of winning $20, and then other students respond by bidding up the price.

But then something amazing happens as the auction price starts approaching $20. The remaining bidders realize that they could end up having to pay a lot of money and not win the auction. Imagine that you had bid $19, and another bidder upped the ante by bidding $20. What would you do? Is it better to bid $21 for a $20 prize or to remain silent and pay $19 for nothing?

What starts off as a feel-good exercise to take advantage of a generous professorial offer suddenly becomes a sickening war of attrition, where the last two bidders pay more than what the prize is worth. These games routinely end with the winning bid being 50 percent higher than the value of the prize. Since both the highest and second-highest bidders pay, this means that the professor rakes in about three times the amount being auctioned.

This is an example of what auction theorists call an “all-pay” auction, and it’s a game you want to avoid playing if you possibly can.

But Barry Nalebuff pointed me toward a scary website — called — that seems to be exploiting the low-price allure of all-pay auctions. And it seems to be working.

Swoopo auctions off desirable (gotta have) electronic items (Wii’s, smartphones) for really low prices and with really short fuses — often less than a minute before the auction expires. It’s kind of seductive to watch these fast-paced auctions — because if someone ups the high bid, 15 seconds of extra time is added to the auction length. I found myself waiting to see if a TomTom GPS device would really end up selling for $18.

But there is an important hitch: you have to pay Swoopo $1 every time you bid. This creates an analogous all-pay effect. Swoopo may only sell a Wii for $30, but it might collect an extra $1,000 from bids. This website is a great experiment to see whether sunk costs matter. I’m thinking that someone who has already invested $5 in bidding costs is more likely to keep bidding to “protect” his or her sunk investments.

Of course, there is also the concern that you might end up competing against a Swoopo-bot that outbids you just before the time is about to expire. This is a game that I don’t want to start playing.

Jim Farmer

Interesting that is limited to certain states. Is it considered gambling?


Swoopo seems to have found a pretty ingenious business model.

At least, initially. I imagine many people easily seduced by their low prices will eventually get burned out by the per-bid cost. It would be interesting to learn their bidder turn over numbers.


If it's a game people won't want to play after they learned they spent too much bidding then I don't see the rationale for creating For how long does this firm expect to stay in the business? Will they cover their sunk cost before consumers avoid bidding there?

Sam Thornton

Wasted 10 minutes at Swoopo and didn't see anything sell. Once the time remaining drops between 5 and 10 seconds, there is always a new "bid" and an increase in time left.

See for details about the operation.

Looks like an obvious scam to me.

Matt B

Shouldn't this be illegal?


It's like all these 'competitions' with great prizes. The catch is always that it costs a SMS at $1 to participate, so with a few thousand participants the company makes $2000 by giving away a Wii or similar for 'free'.

In Sweden there's a company holding auctions where the lowest unique bid wins the whole thing. Usually every bids costs $10 but they have auctioned away Porsches and other cars, and then the cost of the bid is $100.
I'm sure the swedish Lottery Inspection have a lot to say to those companies.


Also see Marginal Revolution's post yesterday at


There are 100% off and fixed cost auctions. For these auctions there is no reason to ever stop bidding, because the price for the item is not increasing. If I place the winning bid of a 100% off item, that means I get the item, even if that was my only bid, so thus get the item for $1. A quick survey of the site though tells you they are always making a huge profit on these.

If you buy bids in bulk I've heard they are only 75 cents each. Since each bid raises the price by 15 cents, if you see an item selling for $100 that means there has been $500 spent on bids at least.

There are also even worse auctions, like penny bids where each bid (still costs 75 cents) inreases the price by 1 penny instead.

You can also bid on cash or bid on more bids. This seals the fact that this is indeed a gambling site. Apparent from being a brilliant rip off, and perhaps a scam, for their sake, they do advertise as "Entertainment Shopping", so if you derive utility from the auction process, they still provide some value.



@5, No reason it should be illegal unless they are indeed using a a "Swoopo-bot." Unethical? Mmmmm.... possibly, but I still wish I'd thought of it.

Chris Bauman

***Disclaimer - I work for Swoopo***

Hi Ian,

Thanks for taking a look at Swoopo.

Just as a point of clarification, our price per bid is only $0.75. Also, you make a reference to a "Swoopo-bot" in your article. I have a felling that you are referring to our BidButlers. Each BidButler is activated by bidders iin each auction. No one at Swoopo places any BidButlers to drive up prices.

@Ben- The sheer nature of an auction is that you can have only 1 winner. With that said, in the US alone, we have shipped out thousands of won items to our bidders (many of them are repeat winners/bidders, too). On average our winners save over 65% off the retail price. More than the economics is the thrill of the hunt to grab a great deal. For many, that is worth the price of admission.

Matt B

Swoopo also has auctions of packages of bids - an auction of 500 bids for example.

So essentially you are bidding (and paying 75 cents for each bid) to purchase a block of 500 bids to use for another auction in the future. Swoopo makes 75 cents for each bid on this intangible, limitless product - 500 bids.

What is the code to Swoopo of 500 bids? $0.00.

With this type of auction, Swoopo is essentially just printing free money thanks to it's users.


Why would bidding on a "100% off" item ever end? I mean, assuming that people are irrational enough to start bidding in the first place, why would they become rational enough to stop later?

Perhaps there's a certain probability that nobody remembers to bid in time, and eventually it happens?

David Smart

I just saw $80 cash auctioned off for $22.50 - however, it was a "100% off" item, meaning the winning bidder actually pays ZERO for the item itself and is only billed for their bids.

$22.50 / 0.15 per bid = 150 bids made * 0.75 per bid = $112.50 into Swoopo's coffers - $80 payout = $32.50 gross for Swoopo.



This is gambling. The closest thing I know of is not an auction, though they conceit to calling it that. Rather, it is a raffle.


If all bidders were perfectly rational, what would be the best bidding strategy? (Of course, every bidder would use that same best strategy.)

It can't be "don't bid at all," because then one bidder could come in and win everything with one tiny bid. It must be something like, "bid with probability 1 in (e times number of bidders)", or something weird like that.


it may be a lot of things, but it is not gambling. it costs you time to bid on something at ebay, here it costs time and cash to place a bid.

going back to ian's question, sunk costs should stay sunk here, and i bet bidders act accordingly. however, the problem might be bidder's inflated expectations on the probability that their next .15 increment bid will win the auction.

travis ormsby

So, inspired by this post, I tried the Dollar auction on the high school kids I teach AP Macroeconomics to.

I felt wrong keeping the money they paid for the $5 I auctioned off, so I returned it to them (would have profited $20 if I hadn't). But the "sickening war of attition" was plainly evident as the last two students realized what they had gotten themselves into.

Trying to figure out an ethical way to play the game for real.

Matt B

"it costs you time to bid on something at ebay"

What does that have to do with ebay not being classified as gambling?

What transaction does not have a time component?


@ 18, i was under the impression that Mike M (#14) considered swoopo gambling because there was a fee to bid. perhaps not.

let's try again. swoopo is not gambling because there is no random element as to who is the winner. the highest bid always wins wouldn't a rational definition of gambling involve some element of randomness?


Nate, the difference is that with Swoopo, you're not actually bidding - all you can do is bump the price by $0.15. If you could actually bid, then you could pay your $.75 to bid $195 for some $200 item, and probably win. If that were the case, it would be much closer to eBay or a real auction house that charges an entry fee. As it is, the final selling price hardly matters -- you win if everyone else decides not to spend any more on bidding. There's really no way to predict that, so in my opinion, it's essentially a raffle with the prize being the difference between the item's retail cost and the final selling price.