Friday, July 02, 2010

EBay and Second Price Auctions

In a second price auction, the winner pays, not his bid, but the second highest bid, or an amount just above it—the lowest price that would have won. In theory, this makes it in each bidder's interest to bid the highest amount he is willing to pay. Bidding less than that changes the outcome for him only if it puts him below what would otherwise have been the second bid, in which case it results in his losing an auction that he would rather have won,.

EBay uses a second price auction, and as far as I can tell by a little casual observation it fails to work in practice according to the theory, which is an interesting puzzle. There is probably published worked attempting to solve it, but I like puzzles and it isn't really my field, so I have been trying to think about this one.

My interest was spurred this morning when I lost an auction. The item was a kard, an indo-persian knife. I used to collect such things, although it's been years since I added to my collection. I happened across this one on ebay, it was a very attractive piece at a very reasonable (current second high bid) price, so I put in a bid on it. When I went to sleep last night mine was the high bid. When I got up this morning someone else had bought it for very slightly above my bid. My impression is that that is a not uncommon pattern—the winning bid coming in at the last minute. I have a bid currently up for a similar piece, in an auction that (unlike the first) terminates at an hour I am likely to be up, and I plan to watch the final minutes and see what happens.

Thinking about it this morning—I had not yet checked the outcome, but I thought it quite likely that I would be outbid—I came up with one theory, then discarded it. That theory started from the fact that, in a second price auction, there is a final bid—a bid made just before the auction closes, late enough so that other bidders cannot use the information provided by that bid to alter their own. Perhaps the optimal strategy involves putting in a low bid, or no bid, early, so that other bidders will think they are winning and so not realize they need to make relatively high bids to get the item, then put in a higher bid at the last minute.

The problem with that theory is that the same logic I started with implies that the last minute bid ought to represent your true value for the item—the highest price at which you would rather win the auction than lose it. If all bidders act that way, we are back with the original situation. And if each bidder expects the others to act that way, he might as well put in his high bid at the beginning, thus saving himself the trouble of getting up early in the morning, or staying up late at night, in order to cast a high bid at the last minute.

There is, however, a fancier version of the theory that might work. Up to this point, I have been assuming that each bidder knows what the item is worth to him. Perhaps that is the assumption that needs to be modified.

Suppose I would rather pay a hundred dollars for a kard like this than not have one, and further suppose I only want one for my collection. If there were only one kard in the world, it would be worth a hundred dollars to me. But if there is more than one, how much this one is worth to me today depends in part on what price, if I don't get it, I would be able to buy one of the others for tomorrow. That in turn depends in part on how much other buyers value such items at. It follows that observing that someone else has made a high bid for the item is a reason for me to reevaluate upward its value to me. A further reason is that high bids on this item signal that it will have a high resale value; since it is possible that I (or my heirs) will some day want to sell it, that also increases its current value to me. The argument is stronger still if I am, not a collector, but a reseller or a speculator, buying the item in order to later sell it.

This argument brings us back to the last minute strategy. Making a high bid early will drive up the auction price, either to the previous bidder's bid (if I am now the high bidder) or to just above my bid (if I am now the second highest bidder). That will provide information that will lead all other bidders to reevaluate the item up, increasing their (current or last minute) bid accordingly. So I postpone my high bid until the last minute of the auction, when it is too late for other bidders to react to the additional information.

This is, I think, a possible explanation of my initial puzzle, but I am not sure it is correct, or even that it explains all the available data. I have not looked carefully enough to be sure, but my impression is that the spread of prices for such items on ebay—antique indo-persian edged weapons—is larger than I would have expected, with prices for similar items ranging over an order of magnitude or so. That is based on a comparison of prices things are currently up for—a lower bound of their selling price in the case of auctions—with the price that the particular item I bid on actually sold for. I have not watched ebay long enough to be sure that is correct, and different items are not of course identical, but it is at least my impression.

That raises a second possibility for what is happening. Suppose the market for any single item of this sort is very thin. Suppose there are lots of people who value it at a hundred dollars, and a small and unknown number—say between zero and five—of enthusiasts who value it at a thousand. On our original model of how a second price auction works, the item would usually go for a thousand dollars—when at least two enthusiasts were bidding. But occasionally there would be one or zero enthusiasts bidding for the item, and it would go for a hundred dollars.

Now suppose you are the seller, and further suppose that you believe that if there is only one or zero enthusiasts in the market for your item today, you can probably do better next month or next year. You might decide to put in a bid yourself at, say, nine hundred and ninety dollars—either explicitly as a reservation price or covertly by pretending to be an independent bidder. The latter option isn't free, since you will have to pay EBay a commission if you end up buying the item from yourself, but it might still be worth doing.

Further suppose that, even for enthusiasts, watching auctions and bidding on them is costly, so that they will only do so if they think they have a good chance of getting the item they bid on for well under its value to them. The seller now has an incentive to use the covert bid strategy—at the last minute—thus enticing people to follow his auctions. And if you suspect, on the basis of bids made prior to the last minute, that there are no enthusiasts out there this time, you might put in your last minute bid at a hundred and one dollars. That not only reduces the commission you will have to pay to EBay, it also signals buyers looking at the auction after the fact that they have a chance of getting a very good deal on your auctions.

Do any of my readers know of published work exploring such theories or offering other and perhaps better ones? Empirical work? EBay provides, after all, a vast volume of real world data on the working of second price auctions, most of which (I presume) could be mined with suitable software at a relatively low cost.


Eric Goldman said...

David, I am not an expert in this literature but I am aware of some of it. I believe the problem is that people actually pay more than their initial reservation price for the sheer joy of winning. This creates a variation of the winner's curse.

In my case, I always bid my maximum reservation price on my first bid and then forget about the auction. Except in very thin markets, I rarely win an eBay auction with that strategy.


tal said...

I think you had the right theory and then incorrectly discarded it, based on a bad assumption. The assumption was:

"And if each bidder expects the others to act that way, he might as well put in his high bid at the beginning"

I bet that most bidders wouldn't expect all (or even most) other bidders to have the time and inclination to be at their computer at the last minute to place a final bid.

SB7 said...

I heard a talk a couple of years back from someone at Microsoft Research about this sort of issue. I wish I could remember who, but for the life of me I can't.

She had a pretty solid explanation from what I remember. What Eric mentioned above was part of it, IIRC: people are buying an item plus the satisfaction of winning. I believe an assumption about winning at the last minute being more pleasurable than winning early may have factored in as well.

Lo Statuz said...

I think this is an example of anchor bias. The current high bid becomes the anchor for at least one bidder, who is then willing to go a little higher. Bidding at the last moment ("sniping") is a widely-recommended strategy to avoid this.

David Friedman said...

To Eric:
I don't believe in the winner's curse, at least in theory--I don't know the empirical literature. A rational bidder will condition his bid on the knowledge that he will only win if everyone bids lower--hence the relevant value is the value conditional on that.

David Friedman said...

To tal:

If you don't expect others to put in a final bid at the last minute, why don't you simply act according to the simple theory--bid your value to start with?

Anonymous said...

I don't know the academic literature but I'm an experienced ebay user. Many bidders do not bid their maximum initially, and will enter a higher bid if they are outbid. Some possible explainations for this are:

(1) They don't understand how ebay works (quite likely for inexperienced users).

(2) The information that someone else is willing to pay more causes a (rational) reevalution of the item's worth.

(3) Less rationally, a bidder may become excited or irritated and bid more than the item is worth. (Excited by the prospect of "winning" against another person; irritated because the considerable effort used to determine whether to bid and how much has been wasted).

In any case, it's always best to bid at the last second.

Bruce said...

Two thoughts.

1. For low-priced items, the joy of winning can be a significant part of the pleasure of buying in e-bay. After all, people play ordinary games for free and want to win. Ebay is a game coupled with a purchase opportunity.

2. I think a lot of people do not have fully-formed preferences. If the current price of an item is very low (say $2), a person might think his maximum willingness to pay is $10. But if several people bid and the price reaches $15, the person might re-evaluate his preferences and increase his willingness to pay. (I really want it, the extra $5 doesn't mean that much to me, if so many people are bidding it might "really" be worth more, etc.)

Phil Birnbaum said...

You lost an auction this morning. The guy who won wouldn't have won if he didn't follow the strategy he did. The reason you lost was the reason his strategy worked.

Bidding at the last minute allows you to take advantage of the fact that at least some other bidders would rather sleep than bid.

Now, the question becomes: WHY would other bidders, if they would rather sleep than bid, not bid their maximum earlier?

Maybe the equilibrium is to not do so. Maybe they maximize their consumer surplus, figuring (say) that there's a 10% chance they'll be asleep instead of bidding, and a 90% chance they'll be awake. Their consumer surplus from the "bid later" case is higher than from the "bid early" case, even taking into account that there's a 10% chance they'll wind up not bidding.

Or maybe it's irrational. In any case, as long as other late-bidders-who-might-not-show-up exist, it's in my interest to wait until the last minute to give myself the best chance at the best price.

(Of course, this doesn't apply if it's a one-of-a-kind item, as you point out in your post.)

dWj said...

Here's a paper by Ariely, Roth, and someone I don't remember comparing Ebay with Amazon auctions, which has different rules.

Glen Whitman said...

I've thought about this problem a lot, having participated in many eBay auctions. As an economist, I knew the "rational" strategy was to bid my true maximum willingness-to-pay. But I quickly realized that didn't make sense after all.

Why? Because the rational equilibrium assumes that everyone understands how the system works, and moreover, that such mutual understanding is common knowledge.

As soon as you have some people who think it might make sense not to bid their maximum WTP, it becomes rational for others to hold off. By bidding high now, you may alert some of those people who bid below their own WTP that they need to raise their bid. So it makes sense to "snipe" at the last minute instead.

Now, suppose that all bidders are in fact rational and understand the game. Even so, this is not common knowledge. You always *might* be in an auction with irrational or confused bidders. So the same logic for sniping applies.

Finally, I'd make the Hayekian point: preferences are not always well-formed, but in fact may be discovered over time. On some occasions, I've bid what I genuinely *thought* was my maximum WTP. But after getting outbid, I reconsidered and realized I was willing to pay more. This could be Eric Goldman winner's curse variant, but as an economist, I'm aware of that possibility and I guard against it... and even so, I've sometimes updated my valuations. The fact that others may do the same provides yet another incentive to snipe.

Jon Leonard said...

One thing to consider is that if you're following the bid-your-maximum-once strategy, there's not much of an incentive to bid early.

Placing a large bid also reduces flexibility. If I have a budget for bidding on stuff, placing a bid early keeps me from bidding on other things, until either I'm outbid or the auction expires. So if I'm browsing for stuff, I'm best off only placing late bids.

It's also entirely possible that it's "just how Ebay works": Lots of people are copying the apparent strategy without really analyzing whether some alternate strategy would work better.

(That in addition to all the other reasons people have mentioned.)

Anonymous said...

Many seasoned ebay bidders use a 'sniping' program to place a last-second bid at a few cents over the then high bid.

Because it is such a late bid, it does not get outbid - if the timing is right - so you can win the auction even if someone else values the item more than you do. What is happening here is that the seller is receiving less than he would without the sniping. The custom of sniping allows the community of buyers to capture more of the economic surplus created by the transaction (and less of the suplus goes to the sellers), which is why this behaviour persists amongst buyers.

Curt C said...

O ebay, there is currently very little reason to bid early except to possibly reserve order cue status.

The downside of early bidding is price changes in a dynamic world while you cant cancel a bid. Lets say you are bidding on a Persian knife, it looks really nice. Then some old timer sells his entire collection on ebay 30 min later, depressing the market price with a large supply of super nice knives. Now, you would realize that your value of the earlier knife changed to the lower.

By making an early bid, you have little to no edge while giving up informational advantages given through time.

Eric Goldman said...

One more thought about the disadvantages of bidding early. A high early bid leaves the bidder vulnerable to sellers' illegitimate shill bids that are solely intended to push the legitimate bid towards its maximum. This may be rare, but it does happen. Eric.

Lo Statuz said...

dWj: Interesting paper. I guess the puzzle now is why eBay doesn't adopt the Amazon rule that an auction ends only after 10 minutes without a new bid.

Kim Mosley said...

If we all were "honest" and put in the price we'd be willing to really pay for an item, then the real value (if that means anything) would become visible. But we don't. We put in the price that we think would be a bargain. If we fail, there will be another day and another knife (or something else to fulfill our need to accumulate objects). As well, the bidding programs contribute to things selling for lower prices than their "value" to the buyers.

RKN said...


My experience squares with yours, I typically bid the maximum I convince myself I am willing to pay, and walk away.

Except I do this as late as possible, assuming of course that my reserve price hasn't been exceeded by that time. If it hasn't, then bidding late has the practical advantage of not allowing much time for other bidders to "sniff" out my reserve price. For example, for an item I bought on ebay some time ago, the bid history revealed at least one frustrated bidder frantically trying to win before he ran out of time. I suspect, tho I don't know for sure, that he would have paid more than my reserve price, but he simultaneously wanted to pay as little as possible.

Justin Liu said...

I often snipe because I want to win exactly one (1) of an item. Suppose I can afford only one antique but there are several I'm interested in on Ebay. I often throw minimum bids on all of them (that I don't expect to win, but probably wouldn''t mind winning multiple auctions at those prices if they're low enough) in order to get those auctions in single display in my account info. Then as the auctions near their end times I put in my true bids because I don't want to accidentally win multiple auctions.

Unknown said...

I often use sniping programs to put in last minute bids. I do not want to help others re-evaluate their preferences and bid up the price. I am very convinced by the argument that people get satisfaction from winning and even the bidding process itself. I have even seen a used item go for more than the price for the same item new on Amazon (for something I was selling - ha ha!)

I tend to buy used comic books, books, and dvds. The comic book (graphic novel) market and dvd markets are probably good ones to study. There are a lot of participants and items get resold (once they have been read/watched) quickly (so buyers definitely factor in the price they could sell the item for in the future in their calculation of the price they wish to pay). There is also a new price (I always check the new price on Amazon before bidding on ebay) that is used as an item. Often items go for very close to the new price (when you take posting costs into account). I frequently lose auctions - is that because I am a better or worse economist?

SheetWise said...

The second price auction, it seems to me, will only work if the bids are sealed. If eBay simply posted the number of bids -- but not the amounts -- I would immediately make my top bid. As the number of bidders went up, I may even raise my top bid -- but I would do it immediately.

I collect archery equipment, and a lot of it goes into the 750-2,500 range. If the auction goes over my top price, I quit watching it. When it's below, I wait until the last minute (second ;)

If the information wasn't being shared, this would be a true second price auction.

Wayne Conrad said...

Some of the comments assume that the last minute bidder is yoked to their computer in order to put in those last-minute bids. However, there are programs that do this on behalf of the bidder. What proportion of those last minute bids are placed by a program, I do not know, but it appears that 15% of winning bids were placed in the last minute:

I stumbled across this, which I'm sure you've seen: "Sniping and Squatting in Auction Markets": .

SheetWise said...

While eBay is paid by the seller -- the seller is paid by the buyer, and they should have an incentive to create the best possible market for both. The interesting question to me is whether sealed or open bids are better for the seller, I think sealed bids would be much better for buyers.

Penny Auction Online said...

Thanks a lot David for explaining this in a so easy way. I going to keep this things in my mind when I will go to eBay next time I'll keep these things in my mind.

Unknown said...

This was really informative. Thank you so much for explaining the hot spots in bidding. I have learned a lot from your entry. More power to you and to your site! I am visiting this site again. Thank you so much!


Unknown said...

I didn't go through all the comments however I decided to answer the question. So forgive me if the answer has already been given. I only read a handful. My answer is based off Game theory and in economics from mathematician John von Neumann and economist Oskar Morgenstern developed during the 1940s and dominant strategy.

Game theory is a study of how people make decisions in situations in which attaining their goals depends on their interactions with others.
This relates to this situation with what's called "Dominant strategy" That means a strategy that is best for a person or firm, no matter what strategies other/'s use.

The point is the dominant strategy is simple you bid the highest you value the item and forget it.

Their are two outcomes to this, in this case the auction.

#1 Someone else bids more,
#2 You are the high bidder.

If you had bid less and followed it all night. You would have still lost not only money, but possibly sleep and time that could be best spent else where. As they have out bid the highest you value the item.

If you bid more during the night than your highest value of the item you are at a negative payoff (paid to much for the item) along with the other issues mentioned. So over all it would be a poor choice to do otherwise. However it is your opportunity costs not mine.

Therefore, a strategy of bidding your maximum value you place on the item is the dominant strategy, other then more (possibly win at any point, now or late at night following it,with negative payoffs) or less (your lose as you bid less then what you valued it at).

You must remember the price you end up paying is equal to the second highest bid.

This doesn't mean it is the strategy that is most used or what will win the bid. However it will bring the most satisfaction since you won't be paying that price for starters, but even if you did it would be okay as it's how much you value it at and if you lose it's also okay because it wasn't worth that price to you.

Anonymous said...