## MatheMUSEments

Articles for kids about math in everyday life, written by Ivars Peterson for Muse magazine.

## March 29, 2007

### Nice Guys Finish First (Sometimes)

There's trouble in the schoolyard. A kid has accused you and your pals of doing something you shouldn't have. You have to decide whether to stick with the gang or go your own way. You're not completely sure you can trust your friends, so you face a tough choice. Mathematicians and economists call this type of problem the prisoner's dilemma: It forces you decide whether you cooperate with others or take advantage of them.

Imagine you and a friend are prisoners. You're in separate cells. Your captors offer each of you the same deal. If you rat on your partner and he stays mum, you go free and he gets 10 years in prison. If you both stay silent, you both get 6 months. If you both rat, you both get 5 years.

You start thinking about the deal. If my partner rats and I stay mum, I'll do 10 years. If he rats and I rat, I'll do 5 years. If he stays mum and I stay mum, I'll do 6 months. If he stays mum and I rat, I'll go free. Hmmmm. No matter what he does, I'm actually better off betraying him.

If you follow this logic, each turns in the other. You both serve 5 years, which is far worse than the 6 months you would have served if you had trusted each other and said nothing.

The same thing can happen when two competing stores cut prices to lure customers or when two countries are in an arms race. Even though the two parties make the best possible choice from their own viewpoint, they end up worse off than they would if they had cooperated.

What about cooperation on the schoolyard? You'll often find yourself in the prisoner's dilemma, and since you learn which kids you can trust, you can figure out better strategies than always ratting. One is called tit for tat. You start off nice, then next time do what your opponent did the last time.

Even though it may sometimes pay to be nasty, over the long term, being nice actually works better. But there is no hard-and-fast rule that guarantees success every time. Strategies that work well in some situations can fail miserably in others. It's tough out there on the schoolyard.

Muse, January 2000, p. 20.