Book Review - Prisoner's Dilemma

What links the H-bomb, playing chicken and the Cuban missile crisis to game theory?

The answer, according to William Poundstone, is the famous game called the prisoner's dilemma (see here for a fun example). His 1992 book Prisoner's Dilemma is not recent (I was a toddler back then) but is still both fascinating and relevant.

Poundstone's approach is to carefully weave together a biography of John von Neumann and a potted history of the nuclear arms race with examples of fun games. The end result is an utterly gripping read (between you and me I read it in lectures) that never fails to surprise (whether you be an economist or normal).

So as not to ruin the book I'll only share one example of H-bomb game theory...

First, read this fun example of a brilliant game to play with your friends.

Now, the 'Dollar Game' is special because it induces buyers regret. Those who bid inevitably wish they hadn't! There is a rapid escalation. Before we know it, both bidders are wishing they were back where they started. But they always have an incentive to go one higher. They do not want to be left in second place. This is not dissimilar to the nuclear arms race.

The analogy starts with America building the A-bomb at the end of WWII. Understandably, Russia could not contemplate being out gunned so they got one. So the USA understandably got more A-bombs. So did the USSR. So America built the H-bomb. So Russia did too. And so on. The starting position led to escalation and both states ended up in a worse position than at the start when neither had any nuclear bombs: They had spent a lot of money on no tactical advantage. If they had coordinated they could have stopped at some point (i.e. just having one A-bomb each). Sadly for both nations this was never likely to happen.

In fact, the more Poundstone delves into the cold war the more analogies crop up. Coincidently (or not) the people who originally created game theory, such as John von Neumann, also created the bomb.

I highly recommend you read Prisoner's Dilemma so that (if nothing else) you can start to see real life conundrums through game theory spectacles, and what spectacles!

Genre: Economics/Behavioural Economics
Accessibility: 10/10
Accuracy: 9/10
Readability: 9/10
Usefulness: 7/10
Verdict: Very, very interesting!

The Monty Hall Problem - Fast Car

This is a probability puzzle named after the American quiz show host Monty Hall. Strictly speaking it's not a behavioural economics puzzle, but I'm interested in what you do...

There are three doors (1, 2 and 3) with one prize hidden behind each one. There is one car and two goats. Obviously, the idea is to get lucky and pick the car. Equally obviously, there is a one third chance of getting the car.

You can pick whichever door you like, for example door 1.

Monty knows where the car is. He has a think. He opens door 3 and reveals a goat.

He then offers you the chance to switch from door 1 to door 2 (or to stick with door 1).

Do you switch from 1 to 2?

When I first faced this problem I said no. I would stick with door 1. I reasoned that now there is a 50% chance of getting it right, and I might as well stick with what I put down first. It turns out that I was wrong.

If you switch to door 2 there is a higher probability of getting the car!

Wikipedia is full of differing explanations for the maths behind it, but I'll explain it in the way I reasoned it out.

At the start of the problem there is a one third chance of picking the car and you pick door 1. Thus there is a two thirds chance that one of doors 2 and 3 have the car. Therefore there is a two thirds chance that when Monty chose the door to open, he had no choice (he could not open the other door as that would have revealed the car).

There is only a one third chance that neither 2 or 3 had the car. In this case Monty could have picked either 2 or 3 to open.

Thus because there is a 2/3 probability that Monty had to open 3 and there is only a 1/3 chance he could have chosen either, we should switch to the one he did not open: door 2.

It took me a long time to work that out. Please let me know whether my explanation is adequate...

Recommended listening:
Fast Car by Tracy Chapman