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!

Game Theory - Steal Away

Game Theory is one of those things almost all of us have heard of but very few have been able to learn about. It's hugely important in economics, especially the behavioural side of things. So, here is a very brief introduction to Game Theory...

Here is a typical two player 'game':

		Player 2
		Steal	Share
Player 1	Steal	1,1	4,0
	Share	0,4	2,2

Both players decide simultaneously, and without communication, what course of action to take in regards to a strawberry milkshake. They can either share it or steal it. The table shows the four possible outcomes, with the numbers representing what economists call 'utility' (the net benefit to each player).

The fair outcome is (Share, Share) as both get a utility of 2, but both players have an incentive to steal. However, if both try to steal it half the milkshake is spilt on the floor.

Imagine you're Player 1... What do you do? What is your strategy?

Economists use something called the Nash Equilibrium to define the likely outcome. A Nash Equilibrium is an outcome where no-one has an incentive to change their strategy. Thus it is stable. We can work out your best strategy as Player 1 by imagining what Player 2 could do.

If Player 2 steals your best response is to steal (as 1 > 0). If Player 2 shares, your best response is to steal (as 4 > 2). Hey presto, you should always steal!

Equivalently, Player 2 should also always steal. Therefore the Nash Equilibrium is (Steal, Steal).

There is clearly a better outcome for everyone involved (which economists call the Pareto-efficient outcome) but economists predict that without coordination it wont be reached.

Of course if we change the numbers we can change the 'game' and thus the outcome. Much more interesting games than this one (which is commonly called the Prisoners' Dilemma) will have to be covered in later blogs.

Recommended listening:
Steal Away by Ozzy Osbourne