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Drinking and the Dollar Auction Game

Presh  Talwalkar writes a very interesting blog, Minding Your Decisions. Recently, he wrote about an interesting application of what game theorists call the "Dollar Auction Game", a lesson about escalation.

"Business drinking provides a fun subject for strategic thinking. My friend told me about a telling experience on a business trip.

He had visited a bar after a long day only to find members from a competitor company show up as well.

The competition greeted him politely and offered to buy a round of drinks.

My friend might have walked away at the start if he had known better.

A careful analysis shows situations like his contain twisted incentives and usually end up horribly for most parties involved. The phenomenon is known as the "irrational escalation of commitment," or simply "irrational commitment."

It concerns how a sequence of rational decisions can end up in a very absurd outcome. These situations are horrible for buyers-even the smart ones (though as a consequence are very useful for sellers or auctioneers).

The implications come from the important dollar auction game. The game was created by Martin Shubik (of Shapley-Shubik fame, an index useful in thinking about Supreme Court appointments and how game theory is helping genetics research)."

Here is Presh's description of the Dollar Auction game.

"Like many economic students, I learned about this game first-hand. My teacher described the game as a chance for us poor students to make a small profit, if we were smart enough.

The game involved my teacher auctioning off a dollar bill to the class.

Bidding started at 5 cents and bids would increase by five cent increments.

There were two main components to the auction.

The auction ends when no one bids higher. The highest bidder pays the price of his bid and gets the dollar as a prize.

The second highest bidder is also forced to pay his losing bid (5 cents less than the winning bid) but gets nothing in return.

My teacher justified the second rule as reflection of true competition.

In many contests, both sides end up paying or expending effort but only one gets the prize. He told us to think about lawsuits, sports competitions, and political donations. It made sense to us, and we soon started the game.

What happened and the "solution"

The bidding began at 5 cents and a hand shot up to claim the bid. Would anyone pay 10 cents? Another hand shot up.

What about 15 cents? Again, another hand shot up. Bidding at this stage seemed harmless because it's an obvious deal to buy a dollar for any amount less.

The twist became clear about when the high bid was 75 cents. Many students started to think about how the second rule-the one requiring the loser to pay-would affect incentives.

What might the second highest bidder think at this stage? He was offering 70 cents but being outbid.

There were two choices he could make: do nothing and lose 70 cents if the auction endedbid up to 80 cents, and if the auction ended, win the dollar, and profit 20 cents.

It's also possible a third person comes and takes the top spot, but that's not an action one can necessarily depend upon. So ignoring this option, the better choice is to bid 80 cents rather than do nothing.

But this action has an effect on the person bidding 75 cent, who is now the second highest bidder. This person will now make a similar calculation. He can either stand pat and stand to lose 75 cents if the auction ends, or he can raise the bid to 85 cents and have a chance of profiting 15 cents.

Again, bidding higher makes sense. Thinking more generally, it always make sense for the second highest bidder to increase the bid.

Such strategy is why the game unraveled pretty quickly. Soon cash-strapped students were bidding more than one dollar and fighting over who would lose less money."

Presh suggests that we should stay away from such escalation games. But can you think of way to stop the escalation?

(Read all of Presh's piece on the dollar auction game, and check the comments for a hint.  But you should subscribe to his blog, also.)

Irrational commitment need not be wrong. Seth Godin accurately notes that "Salespeople and service providers and marketers who are irrationally committed to customer service can completely transform an ordinary experience and make it remarkable."

Like all game theoretic insights, we have learned the tao of irrational commitment - sometimes it is good, sometime it isn't, and only experience can make the difference.

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Full post as published by Misleading Advertising Law on October 01, 2008 (boomark / email).