Game Theory – Mathemafrica

2017 2/3rds numbers game

This is the fourth year that I’ve played the 2/3rds numbers game with my first year maths class. I’m always interested to see how, knowing previous results will affect this year’s results. Of course I am sure that a great deal depends on exactly how I explain the game, and so I imagine that this is the largest confounding factor in this ‘study’.
If you don’t know about the 2/3rds numbers game, take a look at the post here.

Here are the histograms from the last three years:

This year I told the class the mean results from the previous years to see if it would make a difference (as it seemed to last year). This year, the results are somewhat lower:

The winner was thus the person who got closest to 2/3 of 24.4=16.3. This year one person guessed 16, and one person guessed 16.2. Because everyone was asked to write down an integer, unfortunately I can’t claim that 16.2 is the winner, but they will get a second prize.…

By Jonathan Shock| September 22nd, 2017|Courses, First year, MAM1000, Undergraduate|0 Comments

Does knowledge of past years affect the Keynesian Beauty Contest result?

Last year I played the 2/3 numbers game, also called the Keynesian Beauty Contest with my first year maths class. The discussion can be found here: http://www.mathemafrica.org/?p=11143 I wanted to know if, telling my class the results from last year (including sketching for them the histogram of results), would change how they chose their numbers this year. Of course I can’t tell if it changed them, but what is fascinating is that either:

Their guesses (if I didn’t tell them about the results from last year) would have been very different from those last year, or:
They were completely unaffected by knowing what people did last year, which really means that they believed that the rest of the class would have been unaffected.

I plot here the results from the last three years and you can see how similar the results are, year on year.

You can see that the distributions are relatively similar, and the means are extremely close.…

By Jonathan Shock| August 6th, 2016|Courses, First year, MAM1000, Undergraduate|0 Comments

Game Theory can make you money…

I plan on doing some game theory posts in the near future, but for now, see how some very clever tactical thinking can do you wonders…

How clear is this post?

…

By Jonathan Shock| September 8th, 2015|English|0 Comments