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Wednesday, November 17, 2010

Prisoner’s dilemma

Back to playing games… I have previously played a tournament of the prisoner’s dilemma with some of my pupils.

The basic idea is that of two prisoners who cannot communicate before deciding on their strategy. Do they rat on each other? If only one chooses this strategy, he wins and is set free. If both rat on each other, however, they are both lying and both lose. The rational thing to do is to keep quiet, but this depends on co-operation without the possibility of communication beforehand.

I introduced last year’s class to a set of rules for a simple re-iterated version of the game in one class and then the next time we met, they launched into a full tournament.
  • Each pair plays three games and then switches
  • I use the following score matrix (about the simplest version of the game)
Player 2 attacksPlayer 2 stays passive
Player 1 attacksPlayer 1: 0 points
Player 2: 0 points
Player 1: 2 points
Player 2: 0 points
Player 1 stays passivePlayer 1: 0 points
Player 2: 2 points
Player 1: 1 point
Player 2: 1 point

After a warm-up round, I had each player decide on a strategy in advance. The strategy could be as simple as ‘always attack’ or as complicated as they could think of, including principles for modifying tactics as the game progressed.

The idea was to play a round and then get them to revise their rules before playing a second round, hoping that they would eventually hit on the fact that they have to trust each other to get anywhere. I blinked here, however. Discussion in the break made me think that they were a long way from understanding this and I broke off the game. Afterwards, I felt that this was a mistake. I should have just let them play several rounds until they finally got the point. Sometimes, as a teacher you have to accept the fact that learning takes time.

This year, I just taught them the game and then launched into it. Again, after the first round, they could adjust their strategy and then we played another round. They hadn’t hit on altruism as a strategy, but they were certainly learning. It seemed as if they weren’t going to hit on it immediately, and they began to complain and get bored, so once again I broke off the game. Still, they had experienced enough of the game that I could riff off this experience. A ‘teachable moment’.

What does this teach? Well, I think this is one of the places where game theory is really useful for analyzing ‘real life’. Think about teaching the Cold War, when the whole world was in effect involved in a giant high-stakes round of the Prisoner’s Dilemma. To a degree, this can give insight into all social life, since all social life depends on counting on other people to mostly do what they are supposed to. We can almost always be exploited, but the cost of always guarding against exploitation by others is too high. We have to mostly count on most people doing what they are supposed to do most of the time, even though they could be rewarded by misusing our trust and a game like this can be a way to simplify and emphasize this for young people.

Photo credits: Peter Bruce, Mike_tn's

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