Friday, December 19, 2008

Auctions and Incentives: Part I

Recently, one of my favorite writers on Freakonomics, Ian Ayers, wrote a post discussing the economics and game theory principles behind certain types of auctions.

The first one he talked about is what is called a dollar auction. In this auction, the item up for auction would be cash, or something of fixed and common value. Whoever has the highest bid wins the prize, like normal. What is different, however, is that the second place bidder, aka the “first loser,” also has to pay his bid. So consider this scenario: I put a $20 bill up for auction, starting price $1, bid increments in $1. Would you bid? Even understanding the principles of the game, how once you bid, you might have to pay without winning, I bet most people would bid. So let’s say bidding continues on up, along the bid increments, to a high bid of $10. This is a crucial point in the auction, as the next bid determines whether the person auctioning off the $20 makes money (the next bid, at $11, will guarantee the person auctioning off the cash $11 winning bid + $10 losing bid). Keep in mind, in a standard auction, the profit point would be at $20. Here it’s at $10.

If this doesn’t immediately ding a warning bell in your head, then you should think about this a little more. Would you bid on a $20 bill for $11? Would you put up a $20 to get at least $21 back? How can the answer be yes to both? Perhaps the more important question is, if I win on both sides, who is the loser? Now things become clearer: the person who would pay $10 to get nothing is the loser. Someone buys a $20 for $11, and then the person holding the auction gets a free $10, netting $1. But wait, who says the auction has to end? The $10 bidder can bid $12, usurping the $11 bidder and going from the person who nets the least (-$10) to the person who gains the most ($8). It seems like bidding again at $12 is the smart thing to do for the $10 bidder. Unfortunately, yet again, the same incentive now exists for the other player (or even a new player, moving from $0 to $7 net with a $13 bid). Sounds like a breakdown is coming, doesn’t it?

The last possible pivot point would be at $19. At $19 and $18 payout bids, the person with the cash is sitting pretty, having become the top gainer at the $15 bid point (now he stands to gain at least $17). Initially you would think that no one would bid over $20 for a $20 bill, right? But check out how the incentives are right now: the bidder at $18 stands to lose $18. If he bids $20, at least he breaks even. Breaking even vs. losing $18… the choice seems easy. So he’s up to $20. However, that same equation now presents itself to the formerly-top-bidder at $19.. lose $19 or lose $1 by bidding $21? Seems like losing $1 is better than losing $19… so he bids $21! This common scenario, as you’ve probably derived already, of losing the entire bid amount or bidding again for a chance to net $18 more (at this point it’s “less loss”) will never cease to exist in this auction. It becomes a game of chicken, where the winner loses less. Only when one of the bidders determines he will bite the bullet and take his losses, which could possibly be substantial, will the auction end. If it ends with a high bid of $11 or above, the person running the auction makes money. Seems like a pretty easy way to make money if you can convince people to play.

Before we move on to the real life example, let’s consider ways to get out of this as a player. The first solution would be, quite simply, to not play. In suggesting this I am reminded of my sex-ed teachers in high school who loved to say, “The best way to avoid contracting an STD is to practice abstinence.” Well, it’s true here, if you assume the disease to be those crazy incentives. Of course that’s a pretty boring solution… a better solution would be one where a bidder can game the auctioneer right back.

After some thought, the only solution I could come up with would be an early flat bid of $19. Ideally, you would bid first at $19… no one else has played yet, no one stands to lose anything else, and barring the desire to screw you over (and risk entering into that dreaded bidding war, i.e. losing money), no one would probably bid $20 for a $20 bill, being indifferent between the two immediate $0 options. If someone has already bid $1, things become trickier. A $19 bid retains the incentive for the initial person to bid $20 (not losing their $1), at which point the $19 bidder has escalated the game. If the $1 bidder is smart, however, he will realize that the $1 loss is likely the smallest loss he will receive in this game once the following $19 bid has been cast, and won’t bid that $20. However, odds may be that he might only see the immediate impact and bid $20 to save his $1. If I were the $19 bidder, I’d bid up a few times more just to punish him at this point… even if he won with a $26 bid, I’d then chastise him by saying, “See, if you stayed at $1, you would have lost only $1, not $6.” Of course I would have lost $25, but once he bids $20, I’m prepared to lose at least $19 anyway… that extra $6 loss would be there so that I could at least have some dignity by calling the winner stupid. Of course if the bid increment is locked in at $1 per bid (not that suspicious of a regulation, in fact it even sounds like it’s helping the bidders), there would be no possible solution… only to not be in the game.

Those crazy auctions… my next post will discuss, mentioned in the above Freakonomics article. Check it out now if you want. My recommendation, however, is DON'T REGISTER AND DON'T PLAY, but of course do what you want… I’ll explain my sentiments soon. Don’t forget to add yourself to the “follow this blog” list on the top right, to get emails when I make new posts, and see ya next time.

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