Life's a game

If you haven't watched ITV's Goldenballs before, don't worry. All we need to worry about is the end bit, which is shown in the video above. (This saves about an hour of watching Jasper Carrot).

In the final part of the game, the contestants have amassed a prize pool, and can either choose to "split" or "steal". If both contestants choose split, they split the prize money equally. If they both "steal" they get nothing. If one steals, and the other splits, the stealer takes all.

What's the best tactic?

The answer is very similar to the "Prisoner's dilemma", which goes like this:

John and Ron are big-time criminals, and they've both been arrested and kept in separate cells. The police don't have enough evidence to convict them for the big bank job they just pulled off, but they've got enough other crimes to put them in prison for a year each. The police have a cunning plan. They go to John and offer him a deal: if he grasses on Ron, they'll ignore the lesser charges. John gets to walk free, but they can charge Ron for the bank job and put him in prison for ten years. They offer the same deal to Ron. There's one catch though: if they both confess then they'll both get five years in prison.
We can summarise the offers, in terms of the number of years in prison.

The pay-offs in the table show John's pay-off first, then Ron's. So if John confesses and Ron stays quiet (top right), then John gets freedom and Ron gets ten years in prison.
The dominant strategy, also a Nash equilibrium, is for both players to choose confess. This is easy to explain.

Suppose you're John. If Ron stays quiet, then you can either "confess" and get freedom or "stay quiet" and get a one year sentence. Freedom is better, so the best choice here is to confess.
If Ron confesses, then you can either "confess" and get a five year sentence, or "stay quiet" and get a ten year sentence. Five years in prison is better than ten, so the best choice is confess.
The same logic can be applied to Ron (since the case is absolutely symmetrical).
That is the basic underlying principle to game theory.


Returning to Goldenballs, there are four scenarios in the game, and they are laid out below.

Suppose the final prize money is £100, and that you're player one. Like John in the prisoner's dilemma you look at the options facing you. If player two splits, the best option is to steal and take all the money. If player two steals, you have no choice - you will always leave empty handed. So you may as well choose steal.

Theory tells us that steal is the only option to go for, so why did the guy choose to split? We'll leave that for another time.