Optimum strategy for eBay bidding (game theory of auctions)

[mikeph]

Hi, just had a discussion with a friend about this. Just some details,

eBay auctions are some sort of "half-blind" auctions, where the highest bidder wins, but you do not enter your actual bid. The sale price is equal to the maximum the SECOND highest bidder bids, plus a little extra. You do not make a single bid, you enter the maximum you are willing to pay for this item.

For example, if I bid $40 and John bids $30, I win, but the sale price is somewhere around $31. If John upped his bid to $35 I would still win but the sale price might be $36. If he ups his bid to $41 the sale price is $41 and he wins.



So my friend holds the opinion that "sniping" is optimal for getting the lowest price. This is where you bid at the last possible moment. I think that the time of bidding is irrelevant until people begin to react to the dynamics of the information that is available to them (the sale price, and the number of bids, and specifically NOT the maximum bid).

I cannot formulate an example in my head where "sniping", would earn you a lower sale price than the alternative. Can anyone help resolve the issue?

 

[imiyakawa]

I'll try to formulate this on the spot... I have quite limiting knowledge.


Market economics without consideration of market failure would predict that early bidding would cause you to pay a higher price on average. Let's talk about an example. Let's say product A has 8 people wanting it in an auction.
5 bid for the product, 3 snipe VS 8 bid for the product.
Ceteris Paribus, E of price(5 bid&3 snipe) < E of price(8 bid)

However, this assumes rational market players. An early bid of 95% the actualy value may deter irrational market players, and so early bid + snipe is better than just sniping. Although, such case would be extremely rare.

 

[mikeph]

Sorry I don't follow the example. What is E?

 

[imiyakawa]

Sorry I don't follow the example. What is E?

E is the Expected Value of how much you end up paying.
Ceteris paribus is all other things equal.

The expected value for how much you pay for the good if you BID+SNIPE is more than if you just SNIPE, however there are some rare counter-circumstances, such as if you employe a strategy of bidding extremely hard and that deters all other bidders before the completion of the auction. But, such a strategy will unlikely work in reality..

 

[mikeph]

The expected value for how much you pay for the good if you BID+SNIPE is more than if you just SNIPE,

Why?

 

[operationsres]

Why?

I'm not 100% sure, I should've used the world "should", not "will". THis is my homework questions account btw (so I don't get caught out by lecturers).

Anyways, the following can be our starting point. The following model holds for the 1 good being auctioned:

Supply for the good in question is fixed at Q = 1, as the guy holding the auction can't add more to what's being auctioned half way and the good can't be withdrawn (forget reserve prices, the potential for the auctioneer to withdraw, etc, doesn't matter here).

As more people want the item (they bid for it), the demand curve shifts to the right, and the price rises.

So, to get the cheaper price (or find your dominant strategy), you have to keep demand small. This can be achieved through:
(A) Not bidding at all, and sniping.
(B) Bidding because doing so reduces demand due to the irrationality of other players in the auction. E.g. lodging a large psychological bid to deter other irrational players (they're irrational because they've been scared off).

But, in real life, (B) is unlikely to work, it will probably add to demand (oh here I go lodging probabilities a priori to modeling -_-). (A), in my view, is probably more likely than (B) to reduce demand and so get a cheaper price.

So, subjectively speaking, I'd go with (A) until I was shown a good reason why the (B) strategy would achieve better average results.

BUt yeah, you're correct, there would be a way to bid in certain auctions that would achieve a better result than sniping - a (B).

 

[CRGreathouse]

Ignoring minimum increments, eBay's system is just a standard second-price auction with price discovery. I see no particular reason that sniping would be effective.

There is a certain amount of technical difficulty in determining optimal strategy when bid increments are positive, but that can mostly be ignored as they represent a small fraction of the total price. To what extent the irrationalities of auction opponents might play, I can't say.

 

[CRGreathouse]

As more people want the item (they bid for it), the demand curve shifts to the right, and the price rises.

So, to get the cheaper price (or find your dominant strategy), you have to keep demand small. This can be achieved through:
(A) Not bidding at all, and sniping.
(B) Bidding because doing so reduces demand due to the irrationality of other players in the auction. E.g. lodging a large psychological bid to deter other irrational players (they're irrational because they've been scared off).

What makes you think the demand curve shifts? That sounds unlikely to me.

 

[operationsres]

What makes you think the demand curve shifts? That sounds unlikely to me.

I've not studied Game Theory, but bear with me.
This is the way I see it:

1 bidder, $.01.
Millions of bidders, $Mean perceived value + $Herd Irrationality

Even if the curve connecting these two extreme's isn't linear,
Surely 6 bidders poses more demand for the good (shifting the curve for the auction to the right) than 5 bidders?

I don't see a reason for the price-eventuation cuve that connects 1 bidder and 1 million bidders to dip anywhere.

 

[CRGreathouse]

I've not studied Game Theory, but bear with me.
This is the way I see it:

1 bidder, $.01.
Millions of bidders, $Mean perceived value + $Herd Irrationality

Even if the curve connecting these two extreme's isn't linear,
Surely 6 bidders poses more demand for the good (shifting the curve for the auction to the right) than 5 bidders?

You were talking about the demand curve shifting based on the amount you bid (or whether you bid), and that doesn't make sense to me. The amount you bid isn't going to change the population, presumably.

 

[operationsres]

You were talking about the demand curve shifting based on the amount you bid (or whether you bid), and that doesn't make sense to me. The amount you bid isn't going to change the population, presumably.

Well, the demand population would increase. 5 Bidders and 1 Sniper isn't a population of 6. It's a population of 5 + a minimum incremental bid.

I'll try to formalise it in a different way, getting rid of the idea of a shifting D curve. I believe the following is correct.

[[Total expected cost of a good if you're NOT sniping, and you're bidding = [f(A+1)]*u
[[Total expected cost if you are sniping, and NOT bidding = f(A) + minimum incremental bid that eBay allows.

A = the amount of bidders without you.
A+1 = the amount of bidders with you bidding aswell.
u = mean success rate of your bidding strategy/mean failure rate of your bidding strategy.
f(x) = m(x)ⁿ,

where m and ⁿ await a retrospective formulation.
and f(x) is the average price equation for that class of goods in auctions. (Economic conditions have to be weighted for... etc.)

If n>=1 and u<1, you entering the auction as a bidder will not have a positive expected value.
If n<=1 and u>1, you entering the auction as a bidder will have a positive expected value on the price you will pay, assuming you don't mind if you don't win the auction.

However, it doesn't make sense that n<=1. I submit that pretty much every auction will have n>=1, it Makes sense. Although I could be demonstrated incorrect.

 

[tobyjug3]

As a non mathematical ebay user, I find the best strategy is to place a minimum bid, so that I get notifications of outbids and to keep track of the item, then to place a snipe bid of the maximum I will pay. I do not win every auction but at least 75 to 80%.

 

[operationsres]

As a non mathematical ebay user, I find the best strategy is to place a minimum bid, so that I get notifications of outbids and to keep track of the item, then to place a snipe bid of the maximum I will pay. I do not win every auction but at least 75 to 80%.

That would be suboptimal. It would be better just to pay good attention to the auction as it progresses.

 

[CRGreathouse]

That would be suboptimal. It would be better just to pay good attention to the auction as it progresses.

Why?

 

[CRGreathouse]

[[Total expected cost of a good if you're NOT sniping, and you're bidding = [f(A+1)]*u
[[Total expected cost if you are sniping, and NOT bidding = f(A) + minimum incremental bid that eBay allows.

A = the amount of bidders without you.
A+1 = the amount of bidders with you bidding aswell.
u = mean success rate of your bidding strategy/mean failure rate of your bidding strategy.
f(x) = m(x)ⁿ,

where m and ⁿ await a retrospective formulation.
and f(x) is the average price equation for that class of goods in auctions. (Economic conditions have to be weighted for... etc.)

How can you claim that those formulas are correct (or even meaningful) without defining x, f(x), m, and n? Also, I'm not clear on your definition of u.

How about this: there are an unknown number of others interested in the good. One of them, P_1, is willing to bid up to B_1, and the others are willing to bid only B_k <= B_1. (You don't know which bidder is P_1 or what B_1 is, of course.)

How does sniping compare to bidding your reservation price in the case that the other bidders simply bid "up to" their respective B_i? How does it compare if some of the others (but not B_1) try to snipe? How does it compare if some of the others (including B_1) try to snipe? If you can show me why your strategy is better in these scenarios I may understand you.

 

[operationsres]

How about this: there are an unknown number of others interested in the good. One of them, P_1, is willing to bid up to B_1, and the others are willing to bid only B_k <= B_1. (You don't know which bidder is P_1 or what B_1 is, of course.)

How does sniping compare to bidding your reservation price in the case that the other bidders simply bid "up to" their respective B_i? How does it compare if some of the others (but not B_1) try to snipe? How does it compare if some of the others (including B_1) try to snipe? If you can show me why your strategy is better in these scenarios I may understand you.

That's a nice formulation but it forgets what happens in a real auction. If there is one person, they will bid $0.01, not their personal reserve (aka their B_i). If there is 50 people, and the one that is willing to pay the most has a B_i of $20, in many cases it will go above $20, because of herd dynamics, or because that person doesn't nkow their actually B_i is $20 and is estimating a B_i during a panick (while the auction is closing).

We need a function for the price of a good plotted against the number of people attending the auction.

I'd say it'd be kind of like a sigmoid/square root function. 1 person and the expected price is $0.01. 2 people and that goes up (and sometimes surpasses) to the highest B_i of the 2 people. 50 people and it goes up and sometimes surpasses the highest B_i of those 50 people.

You would have this as your function. :
-----------------------------------------------------------------------------------------
------------
------
---
-

With the roof being the highest B_i out of every single person in the world plus the expected value of herd irrationality.

Although that doesn't answer your question: "Why would any of this cause sniping to be a better strategy".

Well, after reformulating it like this, I withdraw this assertion, because it has become clear that whether you withdraw yourself from the auction or not, your B_i is still in play.

What answers your question is precisely the dynamic of the irrationality in the auction AND the liquidity of the good being sold.

-If you bidding deters people from the auction because they are irrational, you win. (A certain % of these people will have a high B_i).
- If you bid against 1 other bidder, you will pay a higher price, as the expected price you'll pay if you snipe is their bid + an incremental bid, but if you get into a war with them the price will go to the highest of your B_i.
-If you bidding will cause the price you pay to be more because the market is rigid (the price won't be the highest B_i + irrationality amount of the few people in the auction) - there's 2/3 people in the auction and they are spread out over many different auctions looking at the same. You may be able to "swoop in" with a snipe and take the 2/3 bidders looking at many products unawares.

GIven this, I'd recommend sniping in an auction with hardly any bidders.

 

[EnumaElish]

In the "standard" second-price auction model sniping cannot affect the equilibrium outcome.

In a second-price auction each bidder's bid determines his/her probability of winning, but not the price. Should a bidder win, his/her price will be determined by the next-highest bid. Consequently, if all bidders know their valuations with certainty, it makes no difference at which point each one bids his/her valuation.

However, if some bidders are uncertain of their valuations, and look at other bids as information about the value of the object, they can enter into a "bidding war" (the higher the other bid, the higher my own valuation). Here sniping can be an optimal strategy because it guarantees that the sniper will win before the other bidder has a chance to update his/her valuation and enter a higher bid. (This explanation does not require any collusion between bidders.)

This paper explains sniping as bidder collusion: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=232111 (judging by its citation in wiki, the paper posits bidder collusion as an alternative explanation, in addition to correlated values:

Economic analysis of sniping (Roth and Ockenfels, 2000[2]) suggests that it is a rational gain-maximizing (i.e., price-minimizing) strategy for bidders in auctions which fulfill two criteria: 1) the end time is rigidly fixed (such as those on eBay), and 2) it is possible to gain additional information about the "true" value of the item by inspecting previous bids. For example, a novice antiques buyer may prefer to bid in auctions which already have bids placed by more experienced antiques buyers, on the grounds that the items which the experienced buyers are interested in are more likely to be valuable. In this case, more informed buyers may delay bidding until the last minutes of the auction to avoid creating competition for their bids, leading to a lower winning bid.

http://en.wikipedia.org/wiki/Auction_sniping#Uses_of_bid_sniping).

 

[imiyakawa]

So are you saying sometimes sniping has an EV =~ 0, but in some scenarios the EV is > 0, but the EV is pretty much never < 0?

 

[EnumaElish]

So are you saying sometimes sniping has an EV =~ 0, but in some scenarios the EV is > 0, but the EV is pretty much never < 0?

I guess that's the reason why sniping is observed at all.

Suppose sniping has negative expected value for some sniper because, maybe, they're not good at it; suppose that the would-be sniper understands and realizes that their sniping has negative value. In that case, a rational (bad) sniper would not snipe at all, and that negative value wouldn't be observed.

Edit: looking at your earlier post, I realized that "EV" might denote value for the seller, not the bidder. If EV denotes seller's value, then I don't understand how sniping can have EV > 0. To see this, suppose at the last second before an auction is closed, eBay extends it for another 5 minutes.* Suddenly, all sniper bids will have become regular bids and since bidding will continue for another 5 minutes, EV will increase. This demonstrates that by converting snipers into regular bidders you can increase the EV. Therefore the effect of sniping on seller's value has to be negative.

*To hold the total bidding time constant, eBay will ignore the first 5 minutes of bidding.

By a similar argument, in a basketball game "slow play" (~ not bidding) during most of the game followed by "fast play" during the final minutes (~sniping) will have the effect of lowering the final score.

 

[BW338]

Um... I just bid what I want to pay for the item.
Win some. Loose some. :-)

 

[cesiumfrog]

Isn't it obvious that some people decide, after finding themselves outbid on ebay, to raise their maximum further? (Perhaps optimistically they originally bid less than they were potentially willing to pay, or felt less invested in the outcome.) And that (for better or worse.. I guess better for buyers) sniping avoids losing to this behavior.

 

[wil3]

I know very few people who actually bid as their alleged "maximum bid" the maximum that they are willing to pay for the item. Here's why:

1. Some *unethical* sellers intentionally place huge bids on an item with a dummy account, to reveal the highest maximum bid in the item history. They then fill out a mutual bid retraction form with themselves (aka, they claim they mistyped the earlier bid), and then they adjust the bid to be just below the maximum.

2. A lot of people increase their perceived value of the item as the auction progresses. For example, if a lot of other people are bidding on an item, then people are more confident that they are not "overbidding" and become willing to pay more. More bids also indicates that one cannot get a better deal on another listing, as many bids indicates demand is high.

Thus we can assume the the auction model is not a perfect Vichry style but rather some blend of Vichy and English because there is still a moderate amount of bid shading. This means that "sniping" your true maximum bid at the last minute prevents others from upping to their real maximum, allowing one to gain the item at less than what one would get the item at at without bid shading.

Obviously, I'm not an economist, so feel free to flame war this. This is just off of my own personal eBay experiences. I just don't think that eBay auctions fit perfectly into the four mathematical auction models that you learn about in business school.