Sunday, 23 February 2014

Iterated Prisoner's Dilemma Tournament in Class

On Friday my students and I played an iterated Prisoner's Dilemma tournament in class.

This is something that I've run many times before with +Paul Harper during outreach events and I've blogged about it here and +Dana Ernst ran something similar and blogged about it here (both those posts also talk about 2/3rds of the average games).

The way I do this is to split the class in to 4 teams and play a round robin of a set of 5 to 8 repetitions of the Prisoner's Dilemma:



The particular version of the game I usually use is given below:

\[
\begin{pmatrix}
(2,2)&(5,0)\\
(0,5)&(4,4)
\end{pmatrix}
\]

The utilities represent 'years in prison' and over the 3 matches that each team will play (against every other team) the goal is to reduce the total amount of time spent in prison.

This is always good fun and my final year students were no exception (more so that +Paul Harper leant me a sidekick who was allowed to use a Nerf gun when the opposite team defected - more about that here):






In this particular instance we played 8 rounds per 'duel' and it was very helpful to have +Jason Young assist me with writing down the scores etc...

Here's the overall scores which show that the team named: 'Cymru' acquired the least total score (and won a box of chocolate):


Here's all the 'duels':


The 3rd game was the most interesting (from an educators point of view).

Team 'Roy' at the very beginning of the duel stated:

'We will cooperate until you defect, once you defect we will only defect'

Both teams cooperated fully and in the final round Roy defected (whilst their opponent continued to cooperate). This all happened with no prompting from myself which is great because team Roy in effect discovered how strategies had to be defined in repeated games which must take in to account the entire history of the game.

What's also quite cool is that they described 'Tit for Tat' the strategy that won Axelrod's tournaments.

+Michael Trick pointed out that that is completely incorrect and that Roy almost described 'Tit for Tat', they in fact played what's called 'grudger' (which did not win Axelrod's tournaments).

What happened in the last two rounds of the game was also pretty interesting as some coalitions formed to try and share the box of chocolates. Some of my students showed some great game theoretical reasoning: 'we will give you all but enough chocolates for each one of us on the team'...

In class we will consider repeated games in a more rigorous setting and before playing infinitely repeated games also play a modified version of this tournament (I'll blog about that when it happens).

(Note that the name of the winning team: Cymru is Welsh for Wales and I think was partly motivated by the fact that I was wearing my French rugby shirt before the Wales France game that evening. Wales played extremely well and thrashed France.)