Upside-down auction
I just came across tribber.com, which runs bizarre auctions for various products. You submit a single bid, and the winner is the one with the lowest unique bid. The unique part is important — if two people bid 1c and one person bids 2c, then the 2c guy wins. The site basically seems to be a marketing gimmick (I found it via an ad on Facebook).
Since the items for sale have known values, the auctions are common-value with full information (the object is worth the same to everyone and everyone knows how much that is). The optimal bidding strategy seems to depend on the number of bidders. Suppose the object is worth $10 and we have to bid in multiples of $1. If there are two bidders, both will bid $1 and one of them will be the winner (chosen at random). Neither has an incentive to raise their bid since that guarantees a zero payoff.
However if there are three bidders then the equilibrium seems to be that two bid $1 and one bids $2, and the $2 guy wins. A $1 bidder can’t do better by bidding $2 (or more) since the other $1 bidder would then be the winner. And the $2 bidder is worse off if he bids $1 since in that case he’s only the winner with probability 1/3. Bidding higher than $2 doesn’t make sense either. However since the bidders are identical, we can’t say who plays which strategy. So there’ll be a mixed strategy equilibrium where people randomise over bidding $1 and $2.
It gets tedious but I think as the number of bidders increases, people start randomising over a wider range. I think people will always play $1 with some probability, but the weight on higher bids increases with the number of bidders.
Since anyone can enter these auctions, the possibility of getting a Macbook Air for $1 should attract a lot of bidders and reduce the expected returns from playing to essentially zero. As I said it’s a gimmick.
I wonder if tribber borrowed this idea from Felix Salmon?
4 Comments
Dun know about NZ, but all you gotta do is watch Channel 7 and 9 in Aus at 2 a.m. and you get these sort of ads too - lowest unique bid auctions, for iPhones, and iPods and stuff. Also, you have the Girls Gone Wild ads, which I must say, are slightly more entertaining.
I dismiss it as really scammy though. ‘Unique’ is a keyword.
Yes, I agree this has some interesting Game theoretic points, but then again, impractical in real life to the buyers.
For a seller with a screwed up moral compass, this is a brilliant idea.
Something similar is http://www.bidster.com The only difference seems to be that on this website, the winner does not have to pay his “bid”. I think I once figured out that (under some simplifying assumptions) the equilibrium of that game is a mixed strategy with the probability of playing a number is decreasing in the number.
This is a paper on a related auction: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=905606
It’s a “unique bid auction” -
http://en.wikipedia.org/wiki/Unique_bid_auction
There are a few of these running around. You’re right, in that the expected returns would trend towards zero. I found it interesting to see how the auctioneer covers his cost - rather than take any sort of commission, there are various subscription or per-bid fees to be paid.
However, many of these sites have sign-up bonuses. For example, Tribber gives you $500 if you deposit $500. So even if your EV is zero or even a little negative, as long as you don’t mind the variance, it seems like taking the free $500 would be worthwhile.