An iPad for $14.95? Sunk Cost Fallacy and Why People Keep Losing Money in Penny Auctions

A new auction mechanism is in the works these days. The so-called "Penny Auctions" promise people iPads for $14.95 and Marc Jacobs bags for $20. And these auction websites are not lying exactly. There will be a winner, and the winner will end up paying $20 for the bag. But that catch is, there will be countless losers, and we don't have data on their bidding history. And losing, unlike in other auction formats, is not free.

Compare this mechanism to bidding on a painting in an auction room. This is the mechanism that usually appears in the movies, or in novels. An "English auction" is where bids are ascending: In order to be the winner, you have to outbid everyone else. The bids will start low and increase until there is only one bidder standing. In English auctions, the highest bidder will win, but will pay the second highest bid. For example, imagine a painting being auctioned, and there are 10 bidders in the room. The auctioneer opens bidding at $150. People would raise their hands if they are still in. Then the price would go up, say to $200. Some people would drop, and only 6 would remain. The price would go higher yet again, eliminating more bidders. Suppose the price is now $300, and out of the 3 bidders remaining, one of them drops out. There are only 2 left. The auctioneer raises the price to $310. Still 2 bidders remain. The auctioneer raises the price to $320. And one of the two remaining bidders drop. That's where the auction stops, where the winner pays the reservation price of the second highest bidder. We never face the situation where the high bidder would say "I was willing to pay $350 for the painting, let me pay that." The English auction, as long as bids are ascending, will stop when the second highest bidder quits the race, and that becomes the price of the item.

If you lose on an English auction, however, and you don't get the Picasso you'd set your eyes on, you wouldn't have lost anything (maybe other than pride, if you're really rich and if you care about those things). Basically losing doesn't cost you anything monetarily.

In a penny auction, on the other hand, the cost of bidding is 50 cents, and every bid increases the price of the product by 1 penny. There is also a countdown of about 20 seconds that resets with every bid. Let's walk through an example: Say you sit in front of your computer and join bidding on an iPad. The item's price is currently $8.00 and the bidding will close in 5 seconds. There is a countdown. Five-four-three-two... And you place your bid. The clock resets to 20 seconds. The price of the item goes up to $8.01 and you have lost 50 cents. If no one else places a bid for the item in the next 20 seconds, you will win. You have already paid 50 cents for your bid, and you will pay $8.01 for the item.

But what happens when the seconds pass? You wouldn't bid, because you are already the last outstanding bidder. But there is someone else out there who looks at the price, currently at $8.01, and decides to bid. What is 50 cents if you can get the item for such a low price?

Fast forward half an hour, the price of the item is now $11.50. This means, since when you started, there has been $3.50 worth of bids. Since the price is increasing by a penny every time there is a bid, we can deduce that precisely 350 bids were placed by bidders. Say 100 of these were your own. So you did bid 100 times (if not more). That actually costs you $50 (that is, 50 cents per bid, multiplied by 100, the number of your bids). This is a price you've already paid, whether or not you end up with the iPad.

Fast forward another half hour. The price is now $13.40. This means, there's been more bidding, and say you've placed 50 more bids to contribute to the penny-by-penny increase in the price of the item. The iPad is still at an attractive price. You've paid another $25 towards it, and now there is another countdown, the last three seconds, and you are hoping that no one else will bid, so you'll leave this auction with having paid only $50 plus $25 for the cost of bidding, and another $13.40 for the price.

But what happens if someone else bids the last moment, the clock resets, and the price goes up to $13.41? Will you leave, or will you stay? Or, rephrasing the question: Is your likelihood to stay higher, compared to a newcomer, now that you've already spent $75 bidding?

A student of mine ran a penny auction in class, as a part of her term paper. There weren't any experiments run on penny auctions yet (this was last semester, in the Spring of 2011). She hypothesized that the more someone has bid in the past, the more likely they were to stay in the bidding war. She knew by experience: She'd gone to one of these websites and sunk $80 for an item she ended up not winning. To the classroom, she brought $40 in cash. She showed the money to the class, and said she'd run 10 second clocks and give the money to the last bidder. As the professor, I was sitting on one side of the room, recording who was doing the bidding. To simulate the actual penny auctions, we were going to collect 50 cents per bid placed on the $40.

In the end, the student auctioneer made more than $40, of course. The total amount of bids amounted to much more than $40. What happened was that those who already placed bids in the previous rounds couldn't leave bidding.

The idea that "I've already spent so many dollars so I can't leave now" is called the sunk-cost fallacy. The costs are sunk because they are in the past, irretrievable. The feeling is a fallacy because your past bids do not increase the likelihood of winning in the next round. Your likelihood of winning is the same as a newcomer, whether you've spent $60 or $6 on bidding in the previous rounds.

Economists would tell you to always look forward, always make decisions on the margin. They would tell you to always weigh the costs and benefits of the next step you are taking. Yet unfortunately, even the economics students who were taking this seminar in experimental and behavioral economics, to whom we taught rational economic thinking and game theory for months and years, gave in to the sunk cost fallacy. Apparently, forgetting the past was not so easy.