David Weinberger has some thoughts about eBay.
I’ve lost bids to auction snipers. As a customer, I feel cheated, even though, of course, I could take a sniper’s eye-view of the transaction. Even if letting robots game the auction doesn’t affect the integrity of the marketplace, they sure take the fun out of it. And that’s part of eBay’s value as well.
I’ve always wondered why eBay doesn’t use second-price auctions. In a second-price auction, everybody bids the most that they would pay. But the winner only pays the second-highest price. So if I bid $10.02 and I win, but the next highest bidder bid $9.75, then I pay $9.75. Vickrey has a famous paper on the efficiency of such auctions. Because your incentive is to bid your reservation price, a second-price auction actually gets the same revenue as a first-price auction.
The advantage of the second-price auction in the context of eBay is that you don’t have to keep checking to see if someone matched your bid. You just bid once, and you’re done with it.
But David probably would say that what I consider a feature would in fact be a bug. That is, part of the fun (for some people) in using eBay is watching the price change and seeing whether their bid will win.
If they ever start an auction site for soulless dorks who don’t want to be entertained by auctions, they can adopt the Vickrey auction. I’d go for it.
Update: Several commenters point out that “proxy bidding” on eBay works like a second-price auction, and Monte pointed to this paper that ties this to Vickrey auctions. But then I don’t understand why David Weinberger gets annoyed by the “sniper” phenomenon.
For Discussion. Do Vickrey auctions work as well in practice as they do in theory?
READER COMMENTS
Bernard Yomtov
Mar 9 2004 at 9:46pm
eBay does use second-price auctions, or something very close.
You enter the maximum you are willing to pay, and eBay bids on your behalf just enough to keep you as high bidder. So if you are willing to pay $100, say, and the current high bid is $75, eBay bids $75+i on your behalf, where i is the minimum increment- maybe $1. So in effect it is (almost) a second price auction. You bid $100, but pay only $76.
Cap'n Arbyte
Mar 9 2004 at 9:48pm
I think that _is_ how eBay does it. The price you pay if you win is the second-highest bidder’s bid, plus an increment set by eBay that’s related to the size of the highest bid at the time you made your bid. (The increment is to ensure the price moves up in quanta larger than a penny.)
Patri Friedman
Mar 9 2004 at 10:07pm
These users are correct, because of the eBay auction mechanism. Each user enters a maximum, and ebay moves the price up until only one user is left. You can see that the price it reaches is the second price plus one bidding increment. It is not the valuation entered by the user.
The most obvious weakness of such techniques in practice is the worry that the auction house, which earns a revenue proportional to gross auction receipts, will use the information to push up prices by inserting fake bidders.
Patri Friedman
Mar 10 2004 at 1:54am
Some additional thoughts. Note that the standard auction-house bidding mechanism produces the same results as eBay’s method – the second price plus one bid increment. This is because the two people with the highest valuations bid until one drops out because the bid has reached their valuation. I find it quite interesting that this evolved mechanism turns out to be the incentive-compatible one.
Also some more clarification on why incentive-compatible mechanisms are at greater risk for cheating. If customers state their true valuations, the auctioneer can increase gross auction revenue to almost the maximum possible at no risk (*) by faking bids or tipping off the seller as to the highest true valuation. But if customers are stating lower than true valuations, the auctioneer doesn’t know the true valuation, and so can’t push the bid close to it. If the auctioneer pushes the bid past the current one, he gains if it is not yet at the valuation and the customer rebids, and loses if it was at the valuation and the customer drops out.
Even in a Vickrey auction, when there is the possibility of rebidding, if bidders are worried about this risk they shouldn’t bid their true valuations. They should bid lower, and check to see if they need to rebid. (note that without rebidding, the customer risks not winning the item by bidding lower than their true valuation).
Now the really interesting thing is that the standard auction-house method includes the above! That is, it results in a second-price, and has constant rebidding so that no one ever states their true valuation. They simply keep rebidding until it is reached. Hence they are revealing the minimal possible information to the auctioneer, so false bidders have the least information about the risk of losing the sale.
Neat!
(*) no risk assuming he doesn’t get caught. In reality, the potential lost revenue from getting caught cheating will almost certainly outweigh the gains from cheating for any firm in the business for the long-run.
Monte
Mar 10 2004 at 12:24pm
David Lucking-Reiley, Vanderbilt U., wrote an article addressing this very subject, discussing Vickey auctions in practice (primarily focusing on stamp auctions) and e-bay’s attempt, through “proxy” bidding, to follow the second-price, sealed-bid auction model.
Joel
Mar 10 2004 at 6:51pm
Also, the theoretical revenue-equivalence of first-price and second-price auctions depends on the assumptions that buyers are risk-neutral and that they have independent, private valuations.
If buyers are risk-averse (and symmetric) then first-price auctions bring in (on average) more revenue than do Vickrey auctions.
If buyers are asymmetric, then all bets are off.
Bernard Yomtov
Mar 10 2004 at 10:59pm
Joel,
What does “symmetric” mean in this context? And how does risk-aversion enter? Thanks.
jn
Mar 11 2004 at 4:01am
I believe that there is a paper by Roth and Ockenfels (which I can’t find in my files) which discusses why sniping is rational given Ebay’s structure (mainly the hard end which shuts out some bidders if they’re all trying to bid in the last second). I recall that the paper showed that a soft end (something like, the auction is extended for 10 minutes if a bid is made in the last five minutes) eliminates sniping completely.
Joel
Mar 11 2004 at 4:20pm
OK, so the standard auction theory setup is that there are n players, each of whom has a value v_i for the object being auctioned. And the values v_i are drawn from some probability distribution.
So when we talk about independent private values, we mean that each v_i is drawn from some probability distribution F_i and that your draw has no effect on my draw.
This is all very abstract, but imagine that we’re 2 bidders, and that my value is equally likely to be 1, 2, 3 or 4, and that yours is equally likely to be 2, 3, 4, or 5. That fits.
So in this context, symmetric means that all the bidders’ values come from the same distribution. So the example I gave above doesn’t fit, but if our values were both from the same distribution (e.g. equally likely to be 1, 2, 3, or 4) then it would.
Finally, risk-aversion comes into play if your “utility” over money is not strictly linear. Here is a description of the phenomenon. The risk-neutral model assumes, for example, that people are indifferent between $5 for sure and a 50/50 chance of $0 or $10. A risk-averse person would prefer the $5 for sure.
Now, in equilibrium at a first-price auction, people bid below their true value so that they’ll make some profit if they win. But “For a risk-averse bidder, the effect of a slightly lower winning bid on his wealth level has a smaller utility consequence than does the possible loss if this lower bid were, in fact, to result in his losing the auction. Compared to a risk-neutral bidder, a risk-averse bidder will thus bid higher.” (quote from Krishna “Auction Theory” which is a fantastic book if you’re really interesting in the math/econ details)
Anyway, the upshot is that in 1st-price auctions, risk-averse bidders bid higher (in equilibrium) than risk-neutral buyers do, so the expected revenue for the seller is greater. Whereas in 2nd-price auctions, it’s still optimal to bid your true value even if you’re risk averse, so the revenue there is the same.
Way more than you wanted to know, I’m sure. 🙂
Wirkman Virkkala
Mar 11 2004 at 8:20pm
As a sometime eBay bidder and seller, I offer this possible feature for eBay’s bidding.
I often limit my expenditures per month. Often I’d like to bid on, say, three items, and bid once and be done with it. But if I won all three items at my upper limit bid for each, I might overdo expenditures. Rather than rebid for the third item, after I’d lost the previous two, I can imagine eBay offering a two-tiered bid option:
The first bid would be a maximum of, say, $50 for item Z. The second bid for , say, $70, would only kick in if I lost auctions X and Y.
This would be fairly easy to program. And it would allow budgeting by eBayers…. that is, it would automate, somewhat, budgeting by eBayers.
Of course, we can continue what we’ve been doing, and bid a second time on later items, after we’ve surveyed previous auctions.
So, does this illustrate the “income effect” or the “substitution effect” or what?
Bernard Yomtov
Mar 11 2004 at 10:40pm
Joel,
Thanks. Actually, rather than being more than I wanted to know it’s pretty much exactly what I wanted. I’ll get the book.
rvman
Mar 12 2004 at 12:43pm
Annoyance at snipers can be because the snipers are behaving “wrongly” in the same way someone who passes on the right is.(i.e. non-economic motivation)
It can also be economic – if bids are at least partly dependant on other bids, then the sniper, by sniping, is denying rivals information they would use to set their bids. This dependancy can come from competing auctions. If I am setting a bid on a unique or rare item, I bid my valuation. If I am setting a bid on a relatively common item, though, I’m not going to bid more than I think other functionally identical auctions are going to sell for. How do I determine that? By looking at existing closed auctions and open auctions current status. Sniping reduces the amount of information available to set my bid, and thus “annoys” the annoyable.
It will also be annoying in this case, because people who value their time cheaply will always wait to bid late, and thus will win disproportionately often. People with high time values will have to come back and bid in other auctions, or bid higher to compensate. Spending more than they feel they “need” to always annoys people.
Bernard Yomtov
Mar 13 2004 at 7:22pm
Monte,
Thanks for the link to the very interesting paper. I think that many types of economic institutions and practices are much older than we realize, and this gives a smidgen of evidence for that.
Mark Seecof
Mar 17 2004 at 7:53pm
eBay’s proxy-bidding doesn’t give the effect of a Vickrey auction because of “bid retraction.” Instead, the proxy-bidding feature virtually guarantees that the winner will be the bidder with the highest reservation price–and that he will pay that much.
eBay allows a bidder to retract his bid. So the seller employs a shill (or shill account) to bid the price up and up. The proxy-bidding engine will advance the bid until it exceeds any real bidder’s reservation price. Then the shill retracts his last bid, allowing the real bidder with the highest reservation price to win the auction. Repeat sellers who fear detection of their shills have another tactic: they allow the shill to “win” but then claim that the supposed highest bidder (in reality, the seller’s shill) defaulted, and offer the item to the second -highest at his reservation price.
In effect, using eBay’s proxy-bidding service is frequently the same as making an initial bid at your reservation price.
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