The prisoner’s dilemma

You may have heard of the prisoner’s dilemma, one of the cornerstones of game theory. It is a classic example of how two rational individuals might not cooperate, even if it is in their best interests to do so. The prisoner’s dilemma is usually explained like this:

Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with the other. The police admit they don’t have enough evidence to convict the pair on the principal charge. They plan to sentence both to a year in prison on a lesser charge. Simultaneously, the police offer each prisoner a Faustian bargain. Each prisoner is given the opportunity either to betray the other, by testifying that the other committed the crime, or to cooperate with the other by remaining silent. Here’s how it goes:

If A and B both betray the other, each of them serves 2 years in prison
If A betrays B but B remains silent, A will be set free and B will serve 3 years in prison (and vice versa)
If A and B both remain silent, both of them will only serve 1 year in prison (on the lesser charge)

The prisoner’s dilemma is seen in many different areas. In fact, it is almost exactly recreated in Golden Balls, a British game show with a curious name.

In Golden Balls, each person has two choices: Split or Steal.

If  both contestants choose to split the money, they will split the money.

If one chooses to split the money and the other chooses to steal, the stealer gets everything.

If they both choose to steal, nobody wins any money.

Unlike the prisoner’s dilemma, the contestants are actually able to talk to each other before their decision, which produces some great drama. They tend to beg and plead, to say that they are an honest person, that their family would never look at them the same if they lied, that even half of the money is more than enough for them, and so they verbally agree to split. Of course, when they reveal their golden balls, one inevitably steals.

The game produced one of my favorite videos on the internet. It gives you an idea of the psychological terror and drama that goes into these types of decisions. Except something unexpected happens in this one. Here is the link again. Please watch and then come back and read the rest of this blog post.

**

We are now seeing a real life example of the prisoner’s dilemma on the biggest stage – The World Cup. This has required a very specific set of circumstances, and so far they have all happened.

A quick review – the top two teams in each group of four advance to the round of sixteen. The standings are based on points – three points for a win, one point for a draw, zero points for a loss. The tie-breaker is goal differential. Here is how things stand in the United States group.

Germany: 1 win, 0 losses, 1 draw, 4 points, +4 goal differential
USA: 1 win, 0 losses, 1 draw, 4 points, +1 goal differential
Ghana: 0 wins, 1 loss, 1 draw, 1 point, -1 goal differential
Portugal: 0 wins, 1 loss, 1 draw, 1 point, -4 goal differential

There are two games left – Germany will play USA, and Ghana will play Portugal.

In theory, any of the four teams can still advance. But, Germany and the US control their own destiny, so the winner will automatically advance. The loser could still advance, but will need some help in the Ghana-Portugal game.

And now here’s the kicker: if Germany and the US draw, BOTH advance, no matter what happens in the other game.

So, what do you do if you are the US? If you’re Germany? How confident are you that you won’t lose? Do you conspire with the other team? Does Jürgen Klinsmann call up the German head coach and collude?* Do the two teams just sit there for 90 minutes to guarantee a tie?

*This actually happened in the 1982 World Cup, when West Germany and Austria colluded to prevent Algeria from advancing. There was mass protest from fans, but there was no punishment from FIFA. Eventually, FIFA decided that the last two games in each group must be played simultaneously.

This will never happen. It CAN’T happen, because it would be a disastrous ordeal. I think both teams would rather lose than face the consequence of a cheating scandal. Except, is it really cheating? Aren’t you just putting your team in the best position to advance?

It’s an interesting thought.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s