illuminating science

I’ve been doing a little bit of Ebay shopping recently, and have come across some interesting scenarios that got me wondering about the game theory of auctions. Game theory is just what it sounds like - how should you play a game in order to maximise your winnings (or, at least, get the best outcome?) This can be the usual games like poker, naughts and crosses or chess, but it can also be things like deciding how much to sell your new toy for, whether to invest in a certain business, or whether to bother recycling your garbage.

The first interesting auction I found was a guy selling a
$500 gift certificate (actually 10 x $50 certificates, depsite the picture) for Myers, a large department store in Australia. The bidding started at $400, and is now at $416 - only 3 bids so far, but still 10 hours to go, and previous sale of the same thing went for $465! Is it worth bidding on? Clearly, any bid less than $500 is a profitable one provided there’s something you want from Myers. This isn’t quite so clear cut - Myers is quite an upmarket store, and generally is more expensive than other shops, so $500 in Myers might not go as far as $500 in Target, say. And $500 cash in hand is always better than gift certificates that you can only use in a certain store. But there are some things than you can only get in Myers (e.g., some clothes) and some things which are no more expensive than anywhere else (e.g., kitchenware, some appliances). And with no expiry date, and in $50 units, I’m sure you could use them, or even give them as gifts, etc. So probably any bid less than $500 is a good bid. I probably won’t, because I don’t really have $500 I want to tie up right now, but it will be interesting to see where it gets to!

But what is the seller getting out of this? If he actually paid for the vouchers, he’s making a loss. The only reasonable idea I can come up with is that this is a Myers scam to get people to shop there. They’re having a store-wide 25% of sale at the moment, so %10 off Ebay vouchers, with a guaranteed $500 in Myers has to be a profitable venture. And, of course, a limited Ebay release is probably the only way they can do it without people refusing to spend anything except with 10%-off gift certificates! And yet, that means they’re only reaching a pretty limited audience (e.g., 1 a fortnight) - does the resulting advertising contribute enough?

After thining about this, a little Googling turned up an interesting, if somewhat unrelated, mathematical game - the dollar auction. In this game, sometimes run (with hilarious results at business seminars, potential buyers are asked to bid on a $1 bill. They’re allowed to bid any amount, and there’s no reserve (minimum price). There’s only one slight twist: the highest bidder pays her bid and gets the $1 bill, but the second-highest bidder must also pay their bid, but gets nothing in return. So what happens? Well, the first person bids “one cent!” and everyone laughs - what a good deal. Then someone bids “2 cents!” - a natural step, since they still make a good profit. Other people may continue the bidding - after all, just like the Myers vouchers, anything less than $1 is a good deal. For the auctioneer, once bidding gets to about 51 cents, they’re making a profit - they earn 51c from the highest bidder, and (say) 50c from the next, and they’re ahead.

Finally, someone bids 99 cents - and they probably look pretty smug, since no-one is going to bid more than that for a $1 bill. Except, the next highest bidder is caught - they stand to lose 98 cents, as they must still pay their bid. And so, to cut their losses, they bid $1 for a $1 bill. But now the other guy is set to lose 99c! And so, the unthinkable happens - they bid $1.o1, more than the prize is worth! In fact, the entire auction is now unstable - both bidders keep increasing their prices, throwing good money after bad, neither willing to admit defeat. The more proud your bidders, the better the auction goes! Finally, someone decides enough is enough and cuts their losses, and the winner accepts their $1 note, handing over as much as $3 or $4 in its place.

What’s really interesting is that this kind of game might model certain business practices. If you’re competing with another business, then coming second might actually lose you money, and perhaps you’d be willing to accept a loss and come first, to prevent the larger loss associated with coming second. If both businesses are playing this game, then perhaps things escalate! It’s also interesting to note that the auctioneer really wants people to keep bidding - it’s in their interest to stroke the egos of the bidders and encourage them to try and recover their losses. I guess any auction is like that, but here emotions are probably running higher!

Okay, I’m going to take a break for now - I’ll post about my experiences with snipers tomorrow!