The Prisoners’ Dilemma

As you’re sitting at your computer at 7:59 am, sleep deprived, and manically refreshing your Wattle page anticipating that 8 am tutorial sign-up, have you ever wondered how much more sleep you’d get if everyone agreed not to log on until 10 am?

The reason this agreement would most likely fail comes down to the world’s most famous game theory conundrum: The Prisoner’s Dilemma. This theory attempts to explain why individuals often will not cooperate even if it is in their best interests.

This is traditionally presented in a payoff matrix table. Let’s restrict our game to two students, who have the option to ‘Sleep In’ or ‘Sign Up’. If both students sleep in, they’re both better off, so we’ll give this outcome an arbitrary value of 3 for each student (top left square). If Student 2 sleeps in while Student 1 signs up, Student 2 can get more sleep but is disadvantaged because the good tutorial times are most likely taken up, so will be assigned a value of 1. On the other hand, while Student 1 couldn’t sleep in, she is more likely to get her desired tutorial time, so we’ll assign her a value of 4 (top right square). The same applies vice versa (bottom left square). If both students sign up, they don’t get to sleep in and are both worse off, so we’ll assign them each a value of 2 (bottom right square).

Looking at the values, we see that both students will be collectively better off if they slept in and waited for 10 am. However, there remains the temptation for a student to wake up at 8 am to sign up on time as it increases her likelihood of getting that desired time, since everyone else is asleep. Since both students will feel this temptation, and also fear the outcome of waking up at 10 am to find that all the good tutorial classes have already been snapped up, both students will wake up before 8 am to sign up, despite the bleary eyes and throbbing head. They’ll end up in the bottom right corner, collectively worse off. This is the ‘Nash Equilibrium’, which I would highly recommend watching A Beautiful Mind to explore further.

So the next time you’re counting down the seconds and wondering why you’re awake at an ungodly hour, remember that the Prisoner’s Dilemma could explain it all.