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

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

How Much Would You Pay For Facebook? - Time Will Tell

In the first quarter of 2012 the average UK house price was £226,887 (BBC)

How much would you pay for Facebook?

• £1000 a year
• £500 a year
• £100 a year
• £10 a year
• £1 a year
• Nothing

Just £2 a week for one year is enough to equip two African villagers with the skills to work their way out of poverty (Tearfund).

How much would you pay for Facebook?

• £1000 a year
• £500 a year
• £100 a year
• £10 a year
• £1 a year
• Nothing

Now I'm guessing that as you're reading a blog about behavioural economics you're probably on your toes, but similar techniques are used by shops all the time. The next time you go shopping try looking out for them...

Recommended listening:
Time Will Tell by Bob Marley

Cucumber Pimm's - Drink Up Me Hearties

Picture the scene... It's summer. It's dusk. I'm in the garden surrounded by friends sipping Pimm's at a rather splendid birthday party. A friend observed all the fruit in the Pimm's. Cue jokes about it being one of our five a day. It was then that we noticed the cucumber. Why was there cucumber? Was it part of a liberal conspiracy to make us more healthy? Was it just a mistake? Don't get me wrong; the Pimm's tasted great, but why cucumber?

In their highly influential book Nudge: Improving Decisions About Health, Wealth, and Happiness Richard Thaler and Cass Sunstein talk about the potential for using behavioural economics to 'manipulate' people into making objectively better decisions like, for example, eating more healthily. We know that in a canteen placing fruit at eye-level dramatically increases the demand for it.

But surely sneaking cucumber into my Pimm's is immoral?

I'm sure Thaler and Sunstein would immediately point out that they do not advocate tricking or forcing people into eating more healthily. Rather, they propose 'nudging' people to make 'better' decisions. They still want there to be a an open and free choice.

In fairness, the birthday party in question had many drinks on offer. I did not have to choose the fruity Pimm's. I could clearly see there was cucumber present. Perhaps I was just 'nudged' into being healthy...