Business Drinking and the Dollar Auction Game

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 was cautious about the offer–why would they be so nice? As economists point out, there is no such thing as a free lunch (or drink). People have motives and can use gifts to influence a negotiation. The principle applies to a wide variety of situations, from timeshare salespeople to tobacco companies to even food companies (are you surprised that a very common food topping contains morphine?)

My friend quickly guessed the game was one about company secrets. His competitors were trying to get him tipsy so he would leak important information. Far from turning down the offer, my friend estimated he had an advantage in holding his liquor, so instead he escalated the game by offering to buy the second round. It was agreed that payment would alternate for subsequent rounds.

The outcome was something neither side particularly enjoyed. Almost everyone drank too much and was “sick” the next day. As an added insult, the drinks were overpriced and the tab was large. Although my friend had heard important secrets, all the alcohol meant he did not remember them well enough the next day. This proved to be fortunate, however, since it meant his competitors must have forgotten the information he divulged. The game ended with only one clear winner–the barkeeper who sold a lot of drinks. This story illustrates a common ending in this type of game.

Games of escalations

The story is amusing because a small competition turned otherwise smart people into complete fools. Each of them understood the game, the competition, and the strategy. So why did they end up in such a terrible outcome? The answer can be seen by studying an important game of escalation.

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).

It’s a fun game that you can play at parties. It works best with large groups after everyone has had a few drinks.

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.

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

It is the incentives that dictate this weird outcome. Consider an example when the highest bid is $1.50. Since the high bid is above the prize of $1, it is clear no new bidder will enter. Hence, the second bidder faces the two choices of doing nothing and losing $1.45, or raising the bid to $1.55 to lose only 55 cents if the auction ends.

In this case, it makes just as much sense to limit loss as it does to seek profit. The second highest bidder will raise the bid. In turn, the other bidder will perform a similar calculation and again raise the top bid. This bidding war can theoretically continue indefinitely. In practical situations, it ends when someone chooses to fold.

In my class, the game ended around $2 when one player decided to end the madness. But talk to economics professors and you’ll hear that it is not unusual for the game to end at anywhere from $5 to $10. It’s especially juicy if the two bidders dislike each other in social circles, and that adds its own element of entertainment. As a side note, the game can be played in other bid increments too, like 1 cent or 10 cents.

I think the game offers two insights. First, it is best to avoid such games from the outset. And second, if you find yourself in one, cut your losses early. It is better to lose at 2 cents than at 2 dollars.

Can the auction be gamed?

At this point you might be asking if the problem is competition. Could cooperation lead to a good outcome? In theory, yes. It is possible to cut a deal with others to avoid the bidding war. Imagine a class of 9 students who wanted to embarrass a professor. One person could bid a single penny, everyone could agree not to bid higher, ending the game, and the profit of 99 cents could be shared as 11 cents per person.

The solution is promising but the problem is getting everyone to cooperate. Every person has incentive to deviate. Imagine one person who wants to show up the leader. If he bet 2 cents, he has a chance of getting 98 cents for himself rather than settling for the meager split of 11 cents.

Nothing holds players to their words, and when strangers are involved, there is really no guarantee or time to plan in advance. This is why a large lecture hall or sizeable dinner party provide suitable locations to play this game.

I’ve been talking about the game very negatively so far, but there is always another side to the story. Although buyers fare poorly, the auctioneer makes out like a bandit. It’s a trick that makes even rational buyers overspend vast amounts. It’s no wonder that economics professors love to hold this auction.

Key lessons from the dollar auction game:

• Don’t enter such games, or if you do, cut your losses early
• Otherwise rational people can be made to overpay if choices are made in steps that lead to an irrational escalation
• The auction can be gamed if people cooperate, but this is hard to enforce
• It’s good to be the auctioneer

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