## Off & Away, Gambling, and the Strategy of the Dollar Auction

A common demonstration in economics classes is the dollar auction, in which the teacher offers a \\$20 bill to the highest bidder. The twist -- when economists are involved there is always a twist -- is that both the highest bidder and the second-highest bidder have to pay their bids, although only the highest bidder actually gets the \\$20.

What usually happens is something like the following: someone bids \\$1 (which would earn her a profit of \\$19 if she won). Then someone else bids \\$2. The first student, already owing the \\$1 as the second-highest bidder, ups her bid to \\$3, (temporarily) turning a \\$1 loss into a \\$17 profit. This typically goes on for a while, until at some point the bids are \\$20 and \\$19, meaning one student is just breaking even and the other is losing \\$19.

But still at this point, upping the bid to \\$21 turns that \\$19 loss into only a \\$1 loss. Of course it only stays a \\$1 loss if the other student stops bidding; otherwise, the bidding war continues until both students are out quite a bit of money and give up. (This sort of demonstration helps explain why economics professors tend to drive nicer cars than other professors.)

A slight variation on this is the Swoopo-style auction, in which you actually have to pay to increase the bid and become the high bidder. Reimagine the \\$20 bill auction as one where you can pay a \\$4 bidding fee in order to increase the high bid by \\$1 and become the new high bidder. When the auction ends, the winner pays the highest bid, but everyone who bid has to pay the bidding fees.

So, the first bidder might pay \\$4 to start the high bid at \\$1. That means she's on the hook for \\$5 if no one else bids, earning her a sweet \\$15 profit. But now someone else pays \\$4 and increases the bid to \\$2. His (temporary, would-be) profit is \\$14, while our first bidder is still out the \\$4 she paid. If she shells out \\$4 for another bid, then her \\$4 loss becomes (temporarily) a \\$9 profit (\\$20 bill - 2 bids * \\$4 - \\$3 highest bid). And so, even when the highest bid is well over \\$20, a short-sighted low bidder has an incentive (especially if she doesn't reason several steps ahead) to put in another \\$4 in the hopes of getting the \\$20 and making up for some of her loss.

Is there an optimal way to play this game? If you know all the bidders, it makes sense to collude -- agree that only one person will bid and that you'll all split the profits evenly. (Enforcing collusion can be tough in general, but in a game this stacked against the players it shouldn't be tough.)

Otherwise, probably the most sensible thing to do is not to play. But whoever said people are sensible?

Enter Off & Away, which conducts timed Swoopo-style auctions for luxury hotel rooms. Your \\$1 fee makes you the top bidder and increases the top bid by 25 cents. When the time runs out, the top bidder gets the hotel room, while everyone else is just out whatever fees they've paid. (If you bid in the last minute or 30 seconds, the timer resets to a minute or 30 seconds, to give everyone else opportunities to purchase additional bids.)

Now, your bidding fees aren't completely lost. If you've sunk (say) \\$100 in bidding fees into a losing auction, you can apply that \\$100 to purchasing a regular-priced hotel room through Off & Away. However, it's not particularly easy to figure out what hotels and rates they offer. Also, you only have 7 days to do so, and you can't combine failed bids from multiple auctions. My early suspicion is that most bidding fees just end up forfeited.

For instance, here's an auction for two nights at the Wynn. The winning price was \\$189.50, which means that 758 bids were purchased, 23 of them by the eventual winner. That is, the winner paid \\$212.50 for his suite, while the other bidders collectively paid \\$735 for (probably) nothing. Similarly, in the auction for the Presidential Suite at the Pierre, the winner paid \\$938.25 (including \\$182! in bidding fees) while the losers paid a collective \\$2843 for nothing! It's good to be the auctioneer!

Assuming one wants to play in such an auction, what should one do? One obvious observation is that it doesn't make any sense to purchase early. Being outbid is an unambiguous bad -- you're out the bidding fee and you've got nothing to show for it. And if you bid early, you're going to get outbid. In fact, without concocting pretty elaborate (and farfetched) stories about what your bid signals, it doesn't make much sense to bid before the last 30 seconds of the auction.

Naively, it seems like what you'd want to do is wait until 1 second is left on the clock and sneak your bid in right then. Indeed, this seems to be a pretty popular strategy, as the clock tends to get down to 5 seconds or less before a new bid appears. Unfortunately (for the bidders), multiple people seemed to be trying this, as several bids all seemed to hit at once and you'd see the price jump by a dollar or more. Also unfortunately (for the bidders), this cycle seems to happen over and over again. If you are intent on seeing one of these auctions through to the end, then you're signing yourself up to watch the computer for at least an hour after the auction's scheduled end. (I sort of suspect that the typical Off & Away auction ends when all but one of its bidders die of old age.)

As a public service, I spent a fair amount of time watching an auction for a suite at the Mandalay Bay ("retail price \\$1050").

With 20 minutes left, the highest bid was \\$10.75. With 10 minutes left, it had gone up to \\$12. With 5 minutes left, \\$13. And when the clock hit the 1 minute mark, the highest bid was \\$14.75. There were quite a few resets before we hit the all-important 30-second mark, when the highest bid was \\$30. And that's when the magic happened.

The next two hours were an endless cycle of bids and resets, bids and resets, bids and resets. The price climbed to \\$50, then to \\$100, then to \\$150 and \\$200. Finally, at 1:40pm, 100 minutes after the auction was scheduled to end, it went to Eugene M. at \\$224.75 plus \\$82 worth of bids, which seems not bad for a \\$1000 hotel stay. Sad, though, for the other bidders, who are out a collective \\$817 in bidding fees. Total haul: \\$1123.75. Profit (assuming retail price, which is probably not reasonable): \\$73.75. That's not a ton of money, but (based on my folk reverse-engineering of the Amazon Sales Rank algorithm) it's probably more than I made during the same time period.

At any given time, the website shows who placed the few most recent bids, and anecdotally it seemed like people got into short-lived bidding wars before (possibly running out of bid credits or dying and) dropping out and ceding the bidding wars to a new group of people.

I'll be the first to admit that I'm not much of an auction theorist. Sure, I took the course in grad school and could probably still prove any number of theorems about revenue equivalence if you forced me to. But the one really high-stakes auction I participated in (this year's Strangercrombie "We'll Review One Book of Your Choice") I caved when it got too rich for me.

Nonetheless, as a data analyst with travel-industry experience and an advanced degree in economics, I'm shocked (shocked!) that they didn't invite me to help make their evil auctions even more evil, which is the sort of thing I'd be pretty good at. At the same time, I'm trying to be less evil these days, so I might have had to turn them down.

I'm sure that somewhere there are highly-paid lawyers with well-reasoned opinions why this sort of auction doesn't technically count as gambling. Nonetheless, winning one of these auctions seems to rest solely on a combination of dumb luck, lots of time, and lots of money, which (coincidentally) is pretty much the same recipe for winning at a slot machine. A packet of \\$1 Off & Away bids doesn't seem substantially different from a packet of lottery tickets, with the notable exception that you don't have to sit in front of your computer and keep clicking throughout the last two hours of the lottery in order to win.

And so, given our national love of getting something for what seems like nothing but is actually quite a lot, I predict Off & Away will do very, very well. Why the hell didn't I think of it first?

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