Game Theory on TV

This is a great clip from the ITV Game Show Goldenballs hosted by Jasper Carrot. It is about 10 minutes long and the last three minutes are the most relevant. The first seven simply set up the game and lead to the climax.The game is a variation of the Prisoner's Dilemma, though there are major differences.

The similarities are: 1. It is a game of cooperation (share) or defection (steal). 2. Decisions are made simultaneously.

The major differences are: 1. This is a zero-sum game. 2. The players can communicate.

 

Here is some analysis of the decisions involved. Assuming a jackpot of £100k the following outcomes are possible:

 

		PLAYER TWO
		Split	Steal
PLAYER ONE	Split	50k, 50k	0, 100k
	Steal	100k, 0	0, 0

The worst outcome in this game is for the players to both choose ‘steal’ as that would mean no one wins the jackpot. All other scenarios mean the full jackpot is given to at least one of the players. At initial inspection it may appear that the jackpot will be given out ¾ times and no jackpot a ¼ of the time. But the interesting thing with this game is that assuming all players behave rationally the outcome will actually always be that no one wins the jackpot (i.e. two steals).

If you put yourself in the position as a player, you can see how this works. There are two possible options that your opponent can choose (‘steal’ or ‘split’).

Take scenario 1 where your opponent chooses ‘split’. Here if you choose ‘split’ you will get half the jackpot, if you choose ‘steal’ you will get the entire jackpot. So obviously any rational person will choose ‘steal’ as this will maximise your winnings.

Take scenario 2 where your opponent chooses ‘steal’, in this scenario it is irrelevant whether you choose ‘steal’ or ‘split’ because either way you will get nothing. So given the scenario 2 decision is irrelevant (as ‘steal’ and ‘split’ both result in 0) your decision should be based purely on scenario 1 where it has already been illustrated that any rational person will choose ‘steal’.

So the optimum strategy for any player is ‘steal’! Of course the problem with this is that your opponent has the same options as you and therefore will pick ‘steal’ which means the game ends in two ‘steals’. So going back to the game show assuming that all participants are rational human beings the first 55 minutes of the show are irrelevant because whatever the jackpot ends up being the result of the game will always end up with no one wining anything (if the players act rationally).