Monday, 15 June 2015

The Prisoners' Dilemma

One of my Year 4 students asked me to explain a Nash Equilibrium a few weeks ago! I've been thinking about it. I didn't really want to do much explaining. I could only really see myself doing the lesson if I was going to get lots of ideas from the class. So how to open it up?

In the end I decided to go for it. I explained, with a big stone, what an equilibrium is (made easier by lots of the children being French and Spanish), and, briefly, what a dilemma is. Although I'm not overly fond of teaching vocabulary (see comments on Paula Krieg's great post on functions) I'm fine with teaching these words, because they're very easy to explain, and useful words all over the place.

I gave as an example, the famous prisoner's dilemma. I told a story about Albert and Bert, how they stole lots of gold and were arrested. How the police didn't have enough evidence to really put them in prison for a long time. How they took the two off to separate cells and offered to do a deal with each ("It's called 'interrogation," as Rose pointed out).

Another misgiving I'd had was about the morality of all this, the assumption about what a self-interested person does. In the end, I think the whole situation shows how a narrow view of what self-interest is gets us into a pickle, but I didn't want to have to be pressing towards this end.

After the story-telling and word-explaining, we looked at the graphic. Most of the class seemed to get it. In fact there was a lot of un-asked for spontaneous debate about what they would do. I knew I was onto the good stuff! And there we left it for the weekend.

Coming back today, I thought it best to dramatise it, to get the situation really clear in our minds. We split into fours and were cops and robbers. Then I asked them to draw some pictures to explain an equilibrium and a dilemma, and then write a little about what they thought about the situation. While they were doing this I went round and asked them what they thought. Here's a video of one of the drama pieces and some of the thoughts.

I didn't press the point about the Nash equilibrium, though I think it's a fantastic thing to think about. I love how there's a difference between the game theory and what happens in real life (like Annie talking about how she wouldn't rat on her brother). There's lots to explore here for any age. And then there are behavioural economics experiments that are great to explore, like the ultimatum game. I'd like to see more of this intersection between maths, psychology and economics in schools.

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