I tried to introduce the kids to game theory using these slides. We only got as far as the prisoner's dilemma tournament and here's an account of the day.
First of all we started with a "Guess 2/3 of the average" game. We played twice, once with no prior reasoning (just a clear explanation of the rules). Here's a chart of the guesses:
Overall the distribution of guesses is pretty uniform (as is to be expected, right now the students are basically guessing). The average guess was 26 and 2/3rds of the average was 17. Two students happened to win this first round (the two students who actually guessed 17).
Immediately after playing this round I gave an explanation of the fact that all strategies (guesses) other than 0 are dominated (by iteratively eliminating all guesses that are greater than 2/3 of the maximum guess):
Once this had been explained we get the students to play again, here are the results:
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We no longer have a uniform distribution of the guesses and the students are indeed getting it (mostly...). The average guess was now 4 which gives a 2/3 average of 2: so we had a single winner (the student who guessed 2). This was good fun and led to a short discussion of how people are not always rational (as shown by the guess of 14 and 25 in particular).
After this, we went on to look at some videos depicting Prisoner's Dilemmas (these videos are both on the slides link to above):
Going on to explain the logic behind an actual prisoner's dilemma, we proceed to have an Iterated Prisoner's Dilemma tournament:
- Round robin with 4 teams
- Every "duel" was 8 rounds of the Prisoner's Dilemma
- The team with the total lowest score ("years in prison") won the tournament
The first duel (between team "C" and team "D") wasn't that great as the two teams mainly wanted to Defect:
Just at the end of this duel however there was a glimmer of hope! The teams started talking to each other (throughout we were trying to encourage them to talk) and indeed "promised" to both cooperate and of course both defected...
The next few duels (which included team "X" and team "Korea") got a bit more interesting and the teams starting talking to each other, here's the scores:
This next video however is great, both these teams had had a long chat before this duel. As you see team "Korea" defecting before team "D" were expecting them too (at 1:00). and putting themselves in pole position to win the tournament (they did the same trick in the next duel against team "C"):
Going in to the last duel the scores were:
- team "Korea" had 72 points
- team "C" had 82 points
- team "X" had 53 points (with one more duel to play)
- team "D" had 58 points (with one more duel to play)
BUT this is where things got interesting...
Up until here I think the ideas of dominated strategies and equilibria were fairly clear, and I think Paul and I were happy with that. The students however were not and it got slightly personal (all in good humour of course) and the guys in team "X" did not want the leader of team "Korea" to win, so they formed a coalition (a very particular and complex idea in game theory) with team "D" to ensure that team "Korea" did not win. Here's the video of this (at 0:16 the leader of team "Korea" realises what's going on and shouts "I'll buy you a kitkat if one of you starts playing 'D'"):
Here's the final 3 duels of the tournament (including the great play of team "Korea" and the coalition formed at the end between team "D" and team "X"):
The final scores where:
- team "Korea" had 72 points
- team "C" had 82 points
- team "X" had 83 points
- team "D" had 68 points
All in all Paul and I had great fun and the feedback from the kids was great. I think this is a great way of getting some fundamental ideas of game theory across. To shorten the amount of time it takes, we might end up using duels of 4 or 5 rounds instead of 8 but overall we won't change much, in particular having 4 teams works great as it allows time for the non playing teams to try and communicate.
