The Prisoner’s Dilemma
Episode #2 of the course Brain-twisting paradoxes by John Robin
Welcome back to the course. Today as promised, we’re going to land ourselves in jail and see how this can place us in quite a predicament—of the paradox variety!
It’s not your lucky day …
Imagine you just got arrested.
Now, you’re guilty of a minor crime, but your best friend might be guilty of a bigger one. Both of you got arrested together and have been kept in solitary confinement, with no opportunity to communicate.
You’re being interrogated right now. You claim to know nothing and want to speak to your lawyer.
The officer gives you the following choice:
1. Continue to say nothing, in which case, you’ll go to jail for one year for the minor crime.
2. Admit you know your friend is guilty, and you’ll go free, while your friend will get three years.
3. If your friend says you’re guilty too, then you’ll both go to jail for two years.
Do you betray your friend for the chance to go free? Or do you stay silent, hoping your friend will also stay silent—giving you both one year less prison time? And if you stay silent, how do you know your friend will not betray you, giving you three years instead while they walk free?
What do you do?
Take a moment to work it out, then we’ll explore this further.
Exploring the Prisoner’s Dilemma
This scenario is known as the prisoner’s dilemma. As you might have worked out, your most likely course of action is to betray your friend. Here’s why:
If you betray your friend, then there are two possibilities:
• They betray you too, which means you both get two years in prison.
• They don’t betray you, which means you go free.
Staying silent leaves two possibilities:
• Your friend betrays you, which means you get three years in prison.
• They stay silent, which means you go to prison for one year.
Based on the outcomes for these possibilities, you can see why most people would choose to betray their friend. It’s in their best interest: Staying silent guarantees prison time.
On the other hand, even if you consider not betraying your friend, you also will consider what your friend is likely to do: to see this problem exactly how you’re seeing it and choose to betray you in turn, to look out for their best interests. Your likelihood to betray them, to avoid the alternative of going to prison for three years, is therefore higher.
Taking a Team Perspective
This dilemma is incredibly complex, and in fact, whole systems of strategy and analysis have been created to understand it.
The main nuance also explored is how you think of yourself. Are you seeing this problem as a team, or are you seeing it as involving only you? Suppose that instead of being best friends, you and your friend are members of a gang, and you’re thinking of the best outcome for two members of the gang itself. Each year per member is one strike against the gang:
• If one of you betrays the other, then you collectively get three years behind bars.
• If you both betray each other, then you collectively get four years behind bars.
• If both of you stay silent, then you collectively get two years behind bars.
Thinking about the good of the gang, staying silent is the best option—either the gang will lose two years’ worth of members behind bars, or, if your partner betrays you, three years. You’ll likewise assume, knowing your other partner is looking at this like you, that they will not betray you, so you can be reasonably confident that you’ll get out of this with only a total of two years lost by the gang.
This might seem like a strange situation to most, but it’s the heart of how medieval intrigues and other business or political strategy works.
When trust is at stake and your opponent (or partner’s) compliance will affect your wellbeing, deciding to trust them or not can be seen as a form of betray/non-betrayal. If you trust them and you’re wrong, you suffer, whereas if you don’t trust them and you’re wrong, you hurt the relationship. Your choice to trust/not trust depends on what you assume about the other person, and how you view the outcome: your own interests or the interest of the relationship?
I hope you enjoyed this lesson. Tomorrow, we’ll explore a famous paradox. Hint: The name Zeno is involved!
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Read this great article about the business applications of the prisoner’s dilemma.
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