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