How a man broke a British game show using game theory
The “prisoner’s dilemma” is one of the most popular examples of game theory. You and a buddy are arrested for committing a serious crime and are placed in your own cells. The police are offering you both the same deal: if you confess, you’re free, but your boyfriend is going to jail for a very long time (say, 20 years). If you both confess, you both go to jail, but with a lighter sentence (say, five years). If neither of you confesses, the police only have enough evidence to convict you of a minor crime, and you’ll both get a year in jail.
The combinations go like this:
- You admit; my friend does not have: 20 years in prison in total (but zero for you)
- Pal confesses; you don’t: 20 years in prison in total (but zero for them)
- Both confess: 10 years in prison in total (five years each)
- Neither confesses: 2 years in prison in total (one year each)
Obviously, if you can trust your boyfriend not to report you, staying a mom is the best option. But breaking free is very tempting. If you both succumb to this temptation, you will land in prison for five years each (ten years in total). It’s not a particularly good result. So the question basically boils down to this: how much do you trust your friend to keep quiet?
Subscribe to get counterintuitive, surprising and impactful stories delivered to your inbox every Thursday
It’s such an interesting dilemma because it manifests itself in a variety of real-life situations. Game theory is an intriguing combination of probability and human psychology. In the UK, it was even made into a three-year-old game show called gold balls (the pun was definitely intended). And a smart contender beat the show.
Real life prisoners
Assuming you’re not the murderer and thief type, it’s unlikely you’ll find yourself in a police interrogation room anytime soon. But the “prisoner’s dilemma” has a host of real-life applications. Here are some examples.
International relationships. Nuclear weapons are very expensive to manufacture and maintain. Even keeping them is a dangerous business. All nuclear countries would be better off if they could disarm. But doing it unilaterally makes you vulnerable to attack from your rivals. So, until nations can trust each other to disarm, they too will retain their nuclear weapons. The same dilemma applies to any treaty that is unilaterally punitive but multilaterally rewarding – like climate change agreements, for example.
Working hours. In a laissez-faire, an unfettered capitalist system without workplace laws, the prisoner’s dilemma presents itself as a “race to the bottom”. For example, if Bobby works from 9 am to 5 pm, he risks being replaced by Linda, who is ready to work from 8 am to 6 pm. Linda, in turn, could be fired to make way for Lena, who works 8-6 and weekends. It’s better for everyone if employees agree to certain acceptable working hours. Previously, guilds or unofficial workers’ organizations threatened or attacked people who undermined their colleagues by working more. Today, most countries have kind of labor rights. For example, in 2018, a baker in France was fined €3,000 for not taking a day off.
tinder. Tinder is a dating app that requires you to swipe right to “accept” a match, or left to “reject” them. Some people do it honestly – slipping based on deliberate, thoughtful attention to the intended date. Others glide right over everything with the nonchalant air of a lothario. This is a dilemma because if both people are thoughtful swipers, the chances of a successful date are higher. But if both are pathological rectifiers, there will be a lot of unnecessary appointments. Tinder is best when both users take it seriously.
One of the most entertaining variants of the prisoner’s dilemma was the British game show golden balls. At the end of the show, two participants must share a jackpot. The rules are pretty much the same as the original dilemma: if they both split, they get 50% each; if one separates and the other betrays, the divider gets nothing, and the traitor gets everything; if they both betray, they both get nothing. The biggest and most important difference is that the two people can interact, negotiate, promise, cajole and say whatever they want. The traditional prisoner’s dilemma does not allow subjects to collaborate.
Humans are rarely rational agents. Mathematical ideas from game theory like Nash equilibrium or Pareto efficiency are eclipsed by human pride, self-interest, vindictiveness and, quite often, sheer idiocy. With the added element of interaction, gold balls was also a game of manipulation and deception. In one big episode, a contestant cried and looked upset that her rival was stealing, so he promised to part ways. He kept his word, but she betrayed and took all the money.
Break golden balls
One day a man came along and changed the rules of the game. In this particular episode, the £13,600 ($16,600) jackpot was to be split or stolen between Nick and Ibrahim. Usually, the candidates open the negotiations by promising to separate (although neither party knows if they will). Nick, however, takes a different tack. He stares at Ibrahim and says, “I’ll choose the flight…I want you to share, and I promise I’ll split the money with you after the show.” He bluntly admits that he’s going to take all the money.
Despite Ibrahim’s best efforts, Nick does not move. (The unedited version of the negotiations lasts 45 minutes.) Nick resolutely and unflinchingly repeats that he’s going to steal (but will split his winnings afterward). Nick’s art of movement is that he now limits what Ibrahim can do. Either Ibrahim steals, in which case they both get nothing, or he splits up and has to believe he’s going to get Something from Nick. Deep down, Ibrahim must choose between resentment and hope. In the end, Ibrahim chooses the split – after all, trust in Nick is better than nothing. During the big reveal, it turns out that Nick has chosen to go their separate ways as well.
In an interview with Radiolab afterwards, Ibrahim said he entered the show thinking he would fly. Nick’s decision changed his mind, and they both ended up getting out of it. Such is the power of game theory.
Jonny Thomson runs a popular Instagram account called Mini Philosophy (@philosophyminis). His first book is Mini Philosophy: A Little Book of Big Ideas.