Playing games with MSc students

This is the fourth post in a series of posts  (see previous posts here, here and here).

I teach the first 4 weeks of the OR Methods module for our MSc in OR and Stats at Cardiff. One of the subjects I teach is game theory and this year I decided to introduce the subject through the use of the same games I've used in outreach events.

We had 31 participants. The first game we played was the 2/3rds of the average game. Here is the first set of guesses (before we discussed rationality and in essence solve the game together).

You can see that the guesses are pretty distributed across the range from 15 to 82. Three students did seem to notice that something was happening around 2/3rds of 100. The winning guess was 26, which is the highest winning first guess I've had so far.

After this we all went through the fact that 0 is the dominating strategy in this game (through iterated elimination of other all other strategies). Once this was rationalised we played again, here's the second set of guesses:

A few weird things happened, for example someone actually guessed 100 (there was no one guessing a 100 before). I suppose this shows some confusion or perhaps someone was just trying to tell me that they thought this was boring (despite the fact that I used a box of chocolats as a participation bribe... :) ). Otherwise the results are as one would expect and the guesses seem to be clustering a bit towards 0. The winning guess was 10 this time around (3 students had to share the chocolats) which is actually a tie for the highest winning second guess I've had so far.

Here's a quick summary of the 4 games I've played so far:

• School kids (13 participants) - First Guess: 17 Second Guess: 2
• Postgraduate students (80 participants) - First Guess: 18 Second Guess: 10
• OR 54 Delegates (10 participants) - First Guess: 23 Second Guess: 3
• MSc 2012 Cohort (31 participants) - First Guess: 26 Second Guess: 10

After this we put the guesses up for everyone to see and discussed what we expect to happen if we played again (and again). I thought this went well and I've had some of the students say they enjoyed it. I certainly enjoy teaching game theory as it's very "easy" to make come alive. After the 2/3rds of the average game we played a prisoner's dilemma tournament but I won't go in to that here. Here are a few photos showing the students discussing strategies and (hopefully) having fun.

Playing games at OR 54

The 54th conference of the Operational Research Society took place in Edinburgh from the 4th till the 6th of September.

Louise Orpin (Education officer of the OR society: http://learnaboutor.com/) was running a stream on education and thought that her and I could give the same talk we gave at SCOR (see previous blog post here) and I've given many times with Professor Paul Harper during high school outreach events (see previous blog post here). This talk is actually designed for school children. It aims to get kids to understand basic ideas of game theory by playing some games.

When asked to give this talk at SCOR I was worried that the audience (PhD students) would be a bit too "mature" for the talk and think it a bit of a waste of their time. The SCOR talk was a great success though and everyone had fun. When it came to giving the talk at OR54 I was also a bit worried as the audience was even more "mature". All these worries were unfounded as it seems that people just like to have fun and play games. It went well. Here are some of the results.

We did not have a huge audience (10) but still had enough to play the games.

The first game we played is the 2/3rds of the average game. Here's the first set of guesses (before discussing rational behaviour):

The guesses were relatively spread out, 2 groups of participants noted that 66 was 2/3 of 100 and also that 43 was 2/3 of 66 but no 1 guessed lower than 5. The winning guess was 23. After explaining the fact that 0 is a dominating strategy we had the participants play again. Here are the guesses second time around:

As you can see 0 was not uniformly picked but the maximum guess was this time 29 and 7 people guessed 3 or lower. The winning guess was this time: 3.

I've run this with 3 types of audiences now and the winning guess on each occasion were (links are to corresponding blog posts):

• School kids - First Guess: 17 Second Guess: 2
• Postgraduate students - First Guess: 18 Second Guess: 10
• OR 54 Delegates - First Guess: 23 Second Guess: 3

We had fun with this and discussed how such a game was a great way to get basic ideas of rationality and dominance across. 

We then proceeded to play a prisoner's dilemma tournament. We split in to 4 teams and the winning team would be the team with the least total score (I've blogged details about this before see here). It was good fun (always) and there was even a coalition that formed to stop the team, that had my undergraduate intern Jason Young, in it from winning. Here are some photos (thanks to Ian Mitchell for the first 2!) from that part of the day:

The cool venue:

Louise starting us out:

Louise and I with the "C" and "D"s used to cooperate or defect...

The scores (if you look carefully you should be able to notice the coalition - Jason chose the name for team D just to make me twitch...):

The above is just 1 example of an outreach event that works really well in schools (and also with more "mature" participants). If you do want more examples please do take a look at http://learnaboutor.com/. I'm writing this the day before teaching game theory to a new cohort of Cardiff MSc students, I'll be playing the same games with them so will probably post about it again at some point. 

(If you'd like more information on the Conference itself take a look at the #OR54 hashtag on G+).