Excerpts from

Prisoner’s Dilemma

William Poundstone


Possibly the dollar auction strikes you as nonsense. It’s a lot different from a real auction. Don’t think about auctions, then. One way to recognize a dollar auction in real life is that it inspires certain figures of speech: “throwing good money after bad”; persevering “so that it all won’t have been in vain” or because there is no way to quit and “save face”; having “too much invested to quit.”

Have you ever called a busy company long distance and been put on hold for a long time? You can hang up, in which case you’ve made an expensive call for nothing. Or you can stay on the line, paying more with each passing minute, and with no guarantee that anyone will take the call. It’s a true dilemma because no simplistic solution makes sense. Provided you really have to speak to someone at the company and there is no less-busy time to call, you can’t categorically resolve to hang up the instant you’re put on hold. It’s equally ridiculous to say you’ll stay on the line no matter how long it takes. There could be some problem with the switchboard and you’d never get connected. It’s difficult to decide just how long you should wait, though.

At crowded amusement parks, people end up waiting in line an hour or more for a ride that lasts a few seconds. Sometimes you can’t believe you waited in line so long for so little. The reason is the “human-engineered” serpentine queues that prevent patrons from seeing how long the line is. You patiently work your way up to a certain point, then turn a corner and see a whole new part of the line. By the time you appreciate just how long the line is, you’ve already invested too much time to give up.

Allan I. Teger found that dollar-auction-like situations are frequently created or exploited for profit. In his 1980 book, Too Much Invested to Quit, Teger notes, “When we are watching a movie on television only to discover that the movie is poor, we are reluctant to turn it off, saying that we have watched it so long that we might just as well continue to see how it ends.... The television stations know that we are reluctant to turn the movie off once we have begun to watch it, so they will often increase the length and frequency of commercials as the movie progresses. Seldom do we turn off the movie with only 20 minutes remaining, even if the commercials are coming at the rate of one every five minutes.”

Strikes that threaten to ruin both labor and management have much in common with the dollar auction. Each side wants to stick it out a little longer; if they give in now all the lost wages or lost profits would just be money down the drain. The dollar auction resembles architectural design competitions (architects invest their own time and effort designing a prestigious new building, but only the winner gets the commission) and patent races (competing firms invest research and development funds on a new product, but only the first to patent it makes any money). Repairing an old car – playing a few more hands of cards to recoup losses – waiting for the bus a few minutes more before giving up and hailing a taxi – staying in a bad job or bad marriage: all are dollar auctions.

As we’ve seen, these game-theoretic dilemmas have a way of being discovered at an appropriate moment in history. The conventional perception of the Vietnam conflict – particularly the psychology popularly imputed to Presidents Johnson and Nixon – is pure dollar auction. “Winning,” in the sense of improving American interests to a degree that might justify the lives lost and money spent, was scarcely possible. The main agenda was to push a little harder and get a nominal victory – “peace with honor,” so that our dead will not have died in vain. Shubik recognizes the Vietnam war as an “exquisite example” of a dollar auction but doesn’t recall it being an inspiration for the game. He believes the game predated his 1971 publication by some time, which might have put its genesis before the late stages of the war.

More recently, the Persian Gulf war was a rich source of dollar-auction rhetoric. In a January 1991 speech to his troops on the southern front, Iraqi President Saddam Hussein “declared... that Iraq’s material losses are already so great that he must now fight to the end,” according to a Los Angeles Times story (January 28, 1991).

Shubik cites Hussein’s position as a particularly troubling case of the myopia of real leaders in such situations. Both sides in the Vietnam conflict could with some plausibility entertain hopes of holding out and winning. The Iraq conflict was far more lopsided. Iraq fought with a technologically backward army a fraction of the size of the UN coalition’s forces. Iraq’s crushing defeat was predictable, seemingly, to everyone but Hussein. It’s easy to dismiss Hussein as a lunatic. Unfortunately, this brand of lunacy is a prevalent one. People aren’t always good at predicting how others will react to their actions. It’s easy to blind oneself to the consequences.

Dollar auction-like conflicts occur in the animal world. Territorial struggles between animals of the same species rarely lead to fights to the death. Sometimes they are mere “wars of attrition,” where combatants face off and make threatening gestures. Finally one animal gets tired and leaves, conceding defeat. The animal willing to hold its ground the longest wins. The only “price” the animals pay is time (time that might be used to hunt food, mate, or care for offspring). Both animals pay the same price; only the one willing to hold out longer wins the dispute.

The dollar auction bears some resemblance to an iterated prisoner’s dilemma. Topping a bid is defecting, since it betters the bidder’s short-term individual position while hurting the common good. Every new bid chips away at the potential profit. The usual debacle is the result of repeated defection on both sides.

Sometimes the dollar auction is a better model than the iterated prisoner’s dilemma for some of the conflicts conventionally treated as such. Escalation, and the possibility of ruin for both sides, is characteristic of arms races. The “winner,” the nation that builds the biggest and most bombs, wins a measure of security. The “loser,” however, is not only less secure for it; it does not get its “wasted” defense budget refunded, either. Consequently, the second-strongest superpower is tempted to spend a little more money to “close the missile gap.”

The dollar auction hints at the difficulty of applying strategies like TIT FOR TAT. Each bidder is echoing the “defection” of the other! To stop bidding is to allow oneself to be exploited.

You might suppose that the problem is that the bidders aren’t “nice” in Axelrod’s sense. Lay the blame at the door of the first person to defect – that is, the first bidder. But how can you criticize the person who makes the first bid? If no one bids, the ninety-nine-cent profit is wasted.

Many conflicts start this way, with a justifiable action that, in retrospect, becomes the first “defection” in an escalating dilemma. The nuclear arms race between the United States and the Soviet Union started when the United States made a bomb to defeat Adolf Hitler.

William Poundstone, Prisoner’s Dilemma, Doubleday, NY 1992, pp. 262-265.

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