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MatheMUSEments
Nice Guys Finish First (Sometimes)
By Ivars Peterson
Muse, January 2000, p. 20.
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.
| |
|
YOUR
CHOICE |
| |
|
rat |
stay mum |
YOUR
PARTNER'S |
rat |
5
years |
10
years |
CHOICE |
stay
mum |
go
free |
6
months |
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.
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