Why sniping with one's maximum value is the optimal bidding strategy for eBay

As anyone who has even looked at a sample of bids from an eBay auction should know, there are a variety of different strategies that people use when bidding. Some keep increasing their bid over the course of the auction (which is called "nibbling"). Some wait until the very end before making their bid (which is called "sniping"). Some just put a single bid in early and then don't do anything else. Etc.

I will argue here that using the sniping strategy with a bid that is the absolute maximum that you would be willing to pay for the item is, in fact, the best strategy to use. What exactly I mean by best is that it gives you the greatest chance of winning the auction at a price that is less than your maximum value and that it keeps the price that you pay if you do win as low as possible.

What to bid

First off is the advice that is repeated over and over across the eBay site and on just about every eBay fan site that exists. That is, make sure to bid your maximum value, i.e., bid the absolute maximum that you would be willing to pay for the item (at least by the end of the auction).

eBay is effectively a second-price auction. That is, the highest bidder wins the item and pays the second highest bid for it. Yes, that isn't quite how eBay works because the highest bidder can pay up to the increment over the second highest bid because of the proxy bidding system that eBay uses. But the increment is so small relative to the price that you will be paying for the item that I would say that it is simply worth ignoring (unless you really want to go to a lot of trouble that at most will save you like a buck but that most likely will not pay off at all).

(If you really want to make the considerable extra effort to possibly save an amount of money that will be smaller than the increment or if you want to read more about why, otherwise, you should treat eBay's proxy bidding system as a second-price auction, I include additional discussion about such topics below.)

At any rate, as any auction theory, game theory, or experimental economics textbook should tell you, in a second-price auction, you should always, always, without a doubt, bid your maximum value. The proof is actually fairly easy, and I include it below as well.

When to bid

So that settles the question of what to bid. The question then remains -- when to bid? If it were the case that all bidders just bid their maximum values, then it wouldn't matter when you bid. You will win if and only if your maximum value is higher than everyone else's, no matter what order those bids come in at, and you will pay the second highest maximum value. Which is exactly what basic game theory predicts for second-price auctions.

However, it is not the case that all bidders bid their maximum values. A very large number of eBay users, either because they have trouble understanding that they should bid their maximum value or because they have trouble simply figuring out what their maximum value is, adjust their bids repeatedly over the course of an auction in response to the bids of others. That is, they nibble.

The presense of such bidders in eBay makes the decision of when to bid actually quite important because their bids will be different based on what you do, which then affects whether or not you will win and how much you will pay if you do win. So, let's try to understand these people.

Recent behavioral economics research suggests that people do actually have a difficult time determining their maximum value for an item. This is a suggestion that has been somewhat surprising for economists who generally assume that people just know their maximum values. However, it is undeniable that the results that come out of this research are inconsistent with what standard economic theory predicts.

What people do appear to be very good at, though, is determining whether their maximum value is greater than or less than a particular price. That is, I might not know that my maximum value for a new microwave oven is $75, but I know that my maximum value is greater than $60 (because I would buy it if confronted with this price) but lower than $90 (because I would not buy it if confronted with this price). And this of course does make some sense because, as consumers, we gets lots of experience in comparing our maximum values to prices but we do not get much experience in deciding what exactly those maximum values are.

(Some addtional information about this research is included below.)

Then, what happens with people in eBay who behave as this research suggests? They nibble. That is, rather than figuring out what their maximum value is, they go into eBay and look at the current bid (or, if no bids have been put in yet, the starting bid) and decide whether or not their maximum value is higher than this bid. If it is not, then they are done. If it is, then they put in a bid.

The next question is, what bid do they put in? They know to bid something higher than the current bid, but they do not know their maximum value that they should put in. If they make a bid that is higher than their maximum value, then they are in trouble because it is difficult to retract this bid. But if they bid lower than their maximum value, they can always bid more later. As such, there are strong incentives to keep this bid low to make sure that it does not exceed their maximum value.

So they put in a low bid. Then, what happens if they end up not being the highest bidder or if someone else comes along and outbids them? Well, they now look at the new current bid and decide whether or not their maximum value is higher than this bid. If not, they are done. If so, they bid again, and the process repeats itself. As such, we see why we get the behavior in eBay of bidders increasing their bids over and over again. That is, nibbling.

Someone increasing their bid is bad for you if you are another bidder. It lowers the likelihood that you will win the auction, and it makes it so that if you do win the auction, you will end up paying a higher price. Your goal then is to get the nibbler to stop nibbling. What will make him stop? Him being the current high bidder. Why? Because then he will have nothing to compare his maximum value with to help him decide that he should bid more.

So then, what is your optimal timing strategy? To let him be the current high bidder for as long as possible. That is, to put your bid in as late as possible so that the nibbler will not have the chance to make the comparison that will help him decide that him should bid more. Or, in other words, sniping.

Thus, we have that your optimal strategy is to bid your maximum value and we have that you should put it in as late as possible to avoid the possibility of nibblers increasing their bids in response to your bid.

Is sniping fair?

Some people think sniping is unfair. However, note what you do when you put your bid in early enough that the nibblers can respond to it -- you actually help them to get a better sense of what their maximum value is and bid accordingly. Yes, the nibblers are not going to like it if you do not provide them with this help, but there is nothing unfair about not providing this help. You are competing in an auction after all. There is no reason you should help them to win it. So I say, snipe away.

So how do I figure out my maximum value?

It may seem to be a little foolish to nibble, but, in fact, it is difficult to figure out your maximum value for an item, as research suggests, and so it does make sense that so many people would nibble. However, to be the best eBay bidder that you can be, you really should figure out what the absolute maximum is that you would be willing to pay.

To do this, I would suggest "hypothetical nibbling". First, think of some amount that you would be willing to pay for the item, say $70. Then, think very carefully about whether you would be willing to buy the item if the price were to become, say, $5 higher in eBay. If after thinking carefully, you are convinced that you would not be willing to pay the $75, then $70 should be your bid. If you determine that you would be willing to pay $75, then try thinking about what you would do if the price were $80.

Keep repeating this process until you find a value that you would not be willing to pay if that were the price in eBay. Then you will know that your maximum value is below that price. You can then bid either the last value that you decided you were willing to pay, or you can start narrowing your maximum value down into dollars and cents. Perhaps do not attempt to narrow your value down too much, though, because this process will become tedious.

So then, keep the change in value that you use for this procedure meaningful and hopefully the procedure will help you to find your maximum value.

What you are doing with this procedure, of course, is just making a bunch of relative comparisons, which, as mentioned above, people tend to be good at (provided that you can get your brain to focus on them as clearly as it would if you were really making that choice). So you take advantage of the fact that you are good at making relative comparisons and use this to help you with something that you probably are not so good at -- determining your absolute maximum value. And hopefully, that will do the trick...

Two additional comments

One obvious problem with sniping is that in many circumstances, you will not be able to be at a computer connected to eBay right as the auction closes. You may need to be at work, at your kid's soccer game, on an international flight, etc. If so, there are a couple possible alternatives. First, just put your bid in as late as you possibly can. A nibbler might still increase his bid a number of times in response to you, but by bidding as late as possible, you will make the chance of this happening as low as you can. Second, there is apparently software out there that can make bids automatically for you at times that you specify, which would do exactly what you need. Third (this is probably frowned upon by eBay but...) you could get a friend or family member to log in to eBay as you and make your bid for you.

Another possible problem with sniping is that a short-term emergency, like your ISP going offline or the power going out, could happen right when you were planning to make your bid. Then, by the time things come back to normal, the auction is over, and you never got the chance to put your bid in. This undoubtedly is a possibility. However, realistically, it is not very likely, and what I would say is more likely is that, if you put your bid in early, some nibbler will come along and outbid you. If there is an item that you really want and that you feel confident that no one will outbid you for, it probably would be a good idea to be careful and bid early, just in case. However, with eBay being used by millions of people around the world, it should be pretty tough to feel confident enough that you won't be outbid, and as such, I think waiting until the end should still be the best strategy.


Of course
One page about sniping
Another page about sniping
A economic research paper about sniping and nibbling that I think is partly wrong but that inspired me to think about the topic

Further discussion about proxy bidding

With eBay's proxy bidding system, the bid that you make just sets an upper bound on the bid that the proxy can make for you. What the proxy will do is keep raising its bid for you, either until its bid is just above the second highest bid or until its bid hits the upper bound. If you win the auction, you will pay (like a traditional first-price auction) the bid that the proxy has made for you, which will be just above the second highest bid. "Just above" means the amount of the increment above the second highest bid.

The point, of course, is that the increment is trivial enough to be ignored, so we might as well say that the proxy bid that you will pay equals the second highest bid. And so, wa-la, we have a second-price auction.

Even in reserve auctions, the reserve simply functions as another bid (made by the seller), and so we still have that the highest bid (which could be the reserve) wins and that that bidder pays the second highest bid (which could also be the reserve).

Personally I think the idea of a second-price auction is less complicated than the idea of proxy bidding. And so I am skeptical of whether eBay made the best choice in deciding to describe their auctions in this way. But... perhaps eBay used some focus groups or something and found that people (who are accustomed to traditional first-price auctions) generally do have an easier time understanding proxy bidding than second-price auctions. Or, then again, maybe eBay had just never heard of second-price auctions.

If you do, for some reason that would escape me, really want to try to pay less than the increment over the second-highest bid, you can do the following: Repeatedly raise you bid by a very small margin (like a nickel) until you end up being the highest bidder. The proxy bid will never exceed your bid, so rather than the proxy bidding up to the increment over the second highest bid, it will stop at your bid, which, if you make the margin small enough, will be less than the increment.

The problem with this, though, it the time it would take to bid over and over again until you finally end up being the highest bidder. Plus every times that another bidder outbids you, you would have to do this time-consuming process again. And, again, the money you stand to save is quite minimal. Furthermore, if someone comes along at the very end and outbids your bid that is marginally above the next bid, you will not have the proxy automatically trying to outbid them for you because the proxy will be stuck at your lower bid. And so there is a good chance that then you could end up losing.

But... give it a try if you really want.

Proof that you should bid your maximum value in a second-price auction

For this proof, let V denote your maximum value for the item that you are bidding on and let B denote the value of your bid. Whether or not you win the auction depends only on how your bid compares with the the highest of all the other bids. Also, how much you pay if you win the item depends only on the highest of all the other bids. As such, we can ignore all the other bids except the highest of them for this proof. Call this bid H.

Your problem here is to choose a value for B, that is, your bid. You know what V is (provided that you have taken the time to think about it), but you are likely to not know what H is (because you do not know all the bids that other people are going to make). Given this uncertainly about H, then, the question is, what B should you pick, given what V is? What we will see is that no matter what H is, there is no B that will do better than choosing B equal to V.

Case one: H is greater than V

If you bid V, you will not win. In fact, if you bid anything less than H you will not win. If you bid something more than H, you will win, but you will pay more for the item than it is worth to you, which is worse than not winning. So, no matter what number you put in for B, you either end up just the same as if you had put in V or you end up worse off than if you had put in V.

Case two: H is less than V

If you bid V, you will win the item and pay H for it. In fact, if you bid anything greater than H, you will win the item and pay H for it. But if your bid is anything less that H, then you will not win the item, which is worse than if you had won the item. So, again, no matter what number you put in for B, you either end up just the same as if you had put in V or you end up worse off than if you had put in V.

As such, there is no way that making B be different from V could help you, and, in many circumstances, it will hurt you.

For an example, suppose that V is $10. Then, suppose that you bid $9.50. There is a chance that H could be $9.75 and if so, you will be worse off than if you had bid $10. Now, try supposing that you bid $10.50. There is a chance that H could be $10.25 and if so, you will be worse off in this case also than if you had bid $10. However, if your bid is $10, then you will do just as well, and maybe better, as with anything else you could have bid.

Note that for this proof I excluded cases where the variables were equal. It is tedious to go through the equal cases and they really do not provide any insights. Plus, then I would have to make assumptions about who get the item if the bids are equal and I would have to make some continuity argument about how if V is truly your maximum value that then you should feel indifferent between winning the item at a price of V and not winning it at all. So, for these reasons (and because the probability of the variables being equal is quite small anyhow) I omit these cases. But if you want to see the mathematical details, any of the types of textbooks that I mention above should have an appropriate proof.

Additional information about research

The results of the above mentioned research are actually a bit more complicated than what I discuss there, and some researchers suggest that the results can be explained by the notion that people are, in fact, good at determining their values but bad at comparing those values to specific prices. There is some validity to that claim, I think, but I do not think that it applies very well to the nibblers on eBay. Perhaps within the next few years or so, though, the research will be done to determine what is (more or less) the truth and in what contexts it is true.

If you are curious to know more now and you don't mind technical economics writing, these issues come up in the following paper that studies attitudes toward risk. Shane Frederick of MIT talked about these issues quite a bit when I saw him present, but his working paper discussing them does not appear to be online. Other research such as Kahneman and Tversky's research on anchoring and adjustment (see Science 1974) suggests that people generally do a good job of making relative comparisons but not such a good job of estimating absolute values, which provides very good support for the idea that people can compare prices to their maximum values but not determine very well what those values actually are.

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