Today’s Spontaneous Lesson: The Prisoner’s Dilemma

This morning, the kids noticed there was but half a donut and one mini muffin (blueberry) remaining. They attempted to work it out amongst themselves — The Girl suggested they simply split both in half and share. The Boy decided to go double or nothing and suggested that they play Rock, Paper, Scissors for the entire half donut.

Now, we all know how 5 year olds play rock, paper, scissors. Their first choice is almost always rock. Therefore The Boy knows if he just plays paper, he’s going to beat her 99% of the time. She even knows this! So I suddenly hear the tiny sounds of a whimpering girl and call them over to hear what happened.

I let her know that she doesn’t have to go along with what he decides. He doesn’t get to declare that donut-based discussions end in a game that we all know he’s going to win. “Next time, just refuse to play it, ok?” I let her know. Then I tell her the *whole* donut half is hers. The boy grumbles and looks surly. He goes up to his room for a little while.

While he’s gone, I talked to my daughter and let her know I thought it was sweet she wanted to split it with him, and I told her not to change. I also let her know that since she was the first one to ask about the donut, I probably would have given her it anyway.

She walks off and The Boy comes back and we have a talk. I let him know that it isn’t nice at all to take advantage of his little sister that way. It was his actions that caused it to go double-or-nothing and made him lose his part of his donut.

Then, we talk about The Prisoner’s Dilemma. It’s a thought experiment that was invented about 60 years ago to explore why people cooperate or not. The very basic version goes something like this: A crime is committed, like a bank robbery. The police pick up two witnesses, but don’t have enough evidence to charge them and/or convict them of a crime, so they want to get at least one prisoner to talk, or both. So they separate the two suspects and let them know the possibilities. If both prisoners stay quiet, they will probably still be locked up for a month on other charges. If both prisoners rat each other out, they will get three months in jail (the justice system likes easy cases). However, if one betrays the other, but the other stays quiet, the betrayer goes *free* and the silent one spends a year in jail.

At first it can seem difficult to figure out what to do — do you trust your partner? Is he really, in fact, guilty? The thing is, it may not even matter to you if he’s guilty or trust worthy. You may notice that no matter what he does, you’ll spend less time in jail if you betray him. Sneaky of the police, isn’t it? If you don’t see that yet, look at this chart:

B silent B talks
A silent 1 month each A gets 1 year, B goes free
A talks A goes free, B gets 1 year Both get 3 months

No matter what B does, A receives less jail time for talking. If B is silent, talking saves A one month. If B talks, talking will save A *nine* months!

Of course, the actual decision might be based on what B will do to you when he gets out of jail. 😉

There is a lot of research on game theory, and the psychology of envy, where researchers run little games and change the variables to see exactly what it takes to get you to betray your friend, or take the spoils, or whatever. A really interesting study about monkeys show that animals will change their opinions on their rewards based on what other animals get: Monkeys are happy with cucumbers unless other monkeys are getting grapes.

TV game shows even like to play around with game theory. Currently running around the internet is this amusing 6-minute clip from “Golden Balls”. At the end of the game, two players remain, with a pot of money. The very last round requires them to choose to split the money, or steal the money. If they both choose split, they do. If one chooses split and the other chooses steal, the stealer gets the whole pot. If they both steal, no one gets any money. Frequently people choose to steal just because they figure if they don’t get any money, no one else should. They don’t want to end up looking the fool. This guy chose a completely different approach:

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