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Applying Game Theory to Win eBay Auctions

Shopping: The Best Application of Applied Mathematics

By Austin Williams, published Jan 08, 2008
Published Content: 22  Total Views: 136,156  Favorited By: 6 CPs
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Game theorists have made some outstanding developments in auction theory over the past few decades. $32 Billion was made during a British Telcom auction designed by a few good game theorists. It's safe to say they know what they're doing!

Let's look at what Game Theory can do for us when we play the eBay Auction game.

First of all, the eBay actions are winner-pays-loser's-price auctions with a time limit. Here is an example: When the clock runs out, Alice wins the auction for a stuffed animal with a Max Bid of $100. Bob comes in second place with a Max Bid of $50. So, Alice wins the stuffed animal and only has to pay $50. (Actually, Alice has to pay $51, but we'll ignore the extra $1 for simplicity's sake). So it really doesn't matter what Max Bid the winner entered. She will always end up paying Bob's Max Bid (which - by definition - is always lower).

eBay designed these auctions this way because they always result in the exact same outcomes as timed English Auctions (auctions in which each player gradually increases their bid over and over again - until they reach their own Max Bid - then shuts up). The only difference is, you don't have to sit in front of your computer all day gradually increasing your bid. eBay automated that process for you, stopping it's bidding on your behalf either when you win, or when it gets to your Max Bid.

So, the first thing you need to do is determine your real Max Bid for the item that you want to win. You won't tell eBay what this is just yet, but you yourself need to know exactly what that amount is. How do you do this? Start by looking up your item on Amazon.com and nextag.com. Find the lowest price for the item you are bidding on that is offered (include shipping and handling if can). Let's call that price "Price A". It only takes about 3 minutes to look this up. Now find out the cost of shipping and handling that you would have to pay on the eBay item if you won it. Call this price "Ship&Handle". Your Max Bid should be equal to "Price A" minus "Ship&Handle".

Applying Game Theory to Win eBay Auctions

eBay headquarters.

Credit: coolcaeser

Copyright: coolcaeser, via Wikimedia

Comments
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Suburb job with this topic. you need to teach others here how to write articles

Posted on 01/16/2008 at 9:01:38 PM

 
This is why I BIN (Buy it Now). Auctions are much more appealing when you are the seller :) Great article!

Posted on 01/10/2008 at 5:01:06 PM

 
especially after noticing that I'd been beat that way several times; and for readily available products, I usually bid on several until I've "sniped" one for substantially less than its lowest-available price elsewhere on the internet. Thanks for the article though, I'll have to look into more of yours about "Game Theory."

Posted on 01/09/2008 at 7:01:07 AM

 
Scott's right about putting in the same max bid. The first bidder is the one whose max bid is counted. However, eBay will let you know what their current bid is and if it's the same as your max bid (not the next increment up, whether the increment be in $1.00, $.25 or $.01 amounts), then you know that your opponent's max bid has been met and you can simply rebid at the next bid (if you're still interested) and be guaranteed a win... unless someone else beats you of course. On that note, a smart bidding strategy (if you set your theoretical max bid lower than the best available internet price) is to always put a few extra cents on your max bid. i.e. your max bid is really $25... well, instead make it $25.03 just in case someone else's max bid is $25. This way, even if the bidding increments are $1.00 or even $5.00, you'll still win by $.03 and the difference is really insubstantial to you. Anyway, I've "sniped" auctions for a long time now, especially after noticing that I'd b

Posted on 01/09/2008 at 7:01:44 AM

 
Nick: I'm very glad to hear that this information will be put to use! I hope you end up saving a lot of money! I'm glad I could help!

Posted on 01/08/2008 at 9:01:21 PM

 
Wow, this is quite the front page article. It's really interesting, and I definitely fall for the "raising the max bid" deal all the time. I use eBay all the time, and boy it's gonna be fun to start this sniping business. Lets see how cheap I can get me an Xbox 360!

Posted on 01/08/2008 at 9:01:32 PM

 
Response to the tying question. I doubt you can tie. The bids go in increments, so whoever lands on $100 first is the winner. Reminds me of the old game where you throw a baseball bat in the air and see whose hand happens to end up at the top.

Posted on 01/08/2008 at 8:01:20 PM

 
Mo: Fine point indeed (and btw, thanks for the clarifications of the rules surrounding a 'tie'). Playing the auction game is indeed different when the item up for bid is unique (such as an antique, or, as you pointed out, a ticket for a sold-out show). This makes the "actual value" of the item dependent on what *others* think it's worth (kind of like the stock market). In this regards, a rational player's valuation of the item is almost certainly dependent (as there is no third party 'Amazon.com' to tell you how much you can expect to pay for it elsewhere, for there is, likely, no 'elsewhere' at all). In such a case, what ought to be the Max Bid? That for another article!

Posted on 01/08/2008 at 7:01:00 PM

 
BTW, I love snipe bidding! It's a great way to win at a lower amount and always fun to watch multiple snipers bid on your auction :) Great article.

Posted on 01/08/2008 at 7:01:40 PM

 
In the case of two people with the same max bid, the person who entered the higher amount would be the leading bidder and the second person would be considered to have been out bid. But that's not why I wanted to comment - this analysis works at this level if what we're discussing is a widely available item; what of a one of a kind item, say a ticket stub? Game theory is still applicable, just not as compact or simple as in the example of, say a book, or an Ikea desk. Interesting idea for an article.

Posted on 01/08/2008 at 7:01:36 PM

 
Rachel: you raise an interesting point! If Alice Max Bids $100 and then Bob Max Bids $100 also, who is declared the winner? I imagine ties are rare... but they must still occur. Does anyone know who eBay declares a winner in this case? It wouldn't change the optimal strategey, but it would change the wording that Rachel pointed out.

Posted on 01/08/2008 at 7:01:06 PM

 
Can you guess how shocked I am to see that an article on Game Theory made it to the Front Page... and as the main article no less! I'm totally stoked. I also had an article about applying game theory to win a spouse. That one made the front page too! I think I'm on the something.... perhaps Game Theory is coming in to its own... lol!

Posted on 01/08/2008 at 6:01:04 PM

 
"She will always end up paying Bob's Max Bid (which - by definition - is always lower)." It isn't always lower. It can in fact be the same if her Max Bid is the same as his.

Posted on 01/08/2008 at 6:01:58 PM

 
Great information!

Posted on 01/08/2008 at 6:01:55 PM

 
Excellent article. I'm forwarding this to an Ebay maniac I know.

Posted on 01/08/2008 at 6:01:46 PM

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