Tuesday, 11 February 2014

A Rock, Paper, Scissors, Lizard, Spock Tournament in class

I just taught mixed strategy Nash equilibria to my students (http://goo.gl/evmerJ and  http://goo.gl/wMxAoY).

I thought I could use this as an excuse to play a Rock, Paper, Scissors tournament and then someone suggested I play a Rock, Paper, Scissors, Lizard, Spock tournament:



Most students had seen the game but to help us along with the rules I put this up on the board (source: wikipedia):



We then proceeded to play a 16 player knockout tournament that +Jason Young kindly helped run. Student were matched up and played best of 3 rounds with sudden death.

Here are the results (open the image in it's own tab to view it in detail):



Here's a plot of the strategies played during the 1st, 2nd and 3rd rounds:






The overall strategy profile played is here:



We're not quite playing at Nash equilibrium (which would imply a uniformly distributed choice of strategies) but it's not too far off.

Here are the strategy profiles of all matches that won a game:


Thus it looks like a response to these winning strategies would be to play strategies that beat Spock, Rock and/or Lizard. Paper would seem to be an ok bet. 

Here are the losing strategies:


It looks like Scissors was being played a bit too much and losing to Spock and Rock.

This was good fun and hopefully help the students understand what a mixed strategy is.