The prisoner’s dilemma

Imagine you and a partner have successfully robbed a bank. Later, you’re both brought in for questioning by the police and placed in separate rooms. You know they don’t have sufficient evidence to convict either of you for the robbery, so if you keep your mouth shut, all they can do is give you a one-year sentence for a lesser charge. After that, you will get out and can enjoy your loot.

But here’s the twist: the cops offer both you and your partner a deal: If you testify against your partner and he stays silent, you’ll go free and he’ll go to jail for ten years. However, if you both turn on each other, you’ll each get a five-year sentence. What do you do?

This is a classic strategic question that represents game theory, which explores how rational people would respond to such a situation.

In the case of the prisoners, they would almost certainly turn on one another, in which case they’d each get a sentence of five years.

In this scenario there is a clear maximum reward – incriminate the other person, face no jail time and have a chance of keeping all the money. Even if your partner also talks, a five-year sentence is still better than the ten years you would get if you stay silent.

But, in the end, since each person would end up testifying against the other one, it’s the cops who win.

Another branch of game theory is the more straightforward mechanism design. Rather than setting options in the hopes of getting a certain reaction, it forces people to behave in a desirable way.

For example, many employers face the problem of employees not using their vacation time. And employers know that well-rested employees perform much better than overworked ones. The company Evernote went so far as to offer its staff a thousand-dollar bonus for taking time off, but even this didn’t work.

When you apply mechanism design to this problem, you don’t need to figure out ways of convincing your employees. All you need to do is ask yourself how to make them take their vacation.

And the answer is simple: Make vacations mandatory!