Another way to explain the Prisoners’ Dilemma to high school students

The Prisoners’ Dilemma is one of the most interesting problems in game theory. It demonstrates the idea of Nash equilibrium in a stark fashion, and the mathematical requirement is very minimal.

Perhaps its only flaw, if there is one, is the subject matter of criminals and police, which is sexy but not necessarily realistic.

The beauty of the Prisoner’s Dilemma is that it happens all the time. One example was highlighted in a previous article about how the Prisoner’s Dilemma comes up in poker tournaments in Las Vegas.

In this article, I want to highlight another commonplace example, inspired by a dilemma from my high school friend.

A polite host fails

The drama unfolded at a house party. My friend had a horrible time because his social rival was at the party. Normally, the two steer clear of each other as they were going after the same girl “Cindy.” So how did they end up at the same party?

It started when Cindy was deciding who to invite. She wanted to invite all of her friends, and she did not want to take favorites and exclude anyone. She realized it would be awkward if the two guys that liked her attended, so she decided to check first.

She asked each person if it would be okay if she invited the other to the party. Each person said it would be fine, but they both felt awkward and annoyed when they came to the party.

So what went wrong? Why did Cindy’s polite request not work out?

The guys were clearly lying about how sensitive they were. But it struck me why they were lying: they were facing an impossible decision.

The party guest dilemma

Consider the incentives of each guy, when asked the question of whether to come. Here are the incentives they face based on their attendance:

–If only one guy attends, then he wins. The person who stays home looks petty and childish.

–If neither attends, then they both look childish. Cindy expressly invited both, and it would be rude to decline.

–If both attend, then they both save face but have a bad time. It’s the worst possible outcome that each would like to avoid.

From these incentives, it is easy to see why each person would decide to attend. Each reasons as follows: “If the other guy is not going, then it is my chance to go and have a good time. On the other hand, if the other person is going to the party, then I better go as well. I won’t have a good time, but it is better than staying at home and looking childish. Either way, the best thing for me to do is attend, regardless of what the other person does.”

Notice this situation is analogous to the Prisoner’s Dilemma. Each guy has a dominant strategy of attending the party, which is why they both fall for the “trap” of attending. The only real way to win is to try to change the game, perhaps by pursuing another girl.

We all know that kids in high school tend to play games when it comes to relationships. As we cannot possibly avoid these situations, we can at least use these situations as teaching devices.