Using Game Theory to Investigate Segregation in Society
Teacher notes
Before using this resource with your students you will want to check to
ensure that you are comfortable with them viewing the content on the
website and the underlying messages expressed at the end, under
‘Wrapping up’.
Game theory is a branch of applied mathematics which is used in
economics, sociology, psychology and biology. It deals with mathematical
modelling of strategy and behaviour in situations where the decisions which
individuals make are affected by what others might do. The 2001 film A
Beautiful Mind was based on the life of John Nash who won the Nobel prize
for economics for his work on game theory.
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Using Game Theory to Investigate Segregation in Society
“Parable of the Polygons” is a website which uses apps to explore how
areas of cities can become segregated. You may find the apps work better
in some browsers than others – they work in Google Chrome.
The site uses a mathematical model to show that small individual biases
can lead to a large collective bias. This article encourages students to think
about the mathematical model underlying the apps.
The starting assumption is that there are two types of individuals (squares
and triangles), each prefers being in a mixed neighbourhood but is
unhappy if too many neighbours are different.
Use the link http://ncase.me/polygons/ and work through the site. Using a
series of apps, you will start to build an understanding of how certain
parameters may result in segregation.
Take some time to experience the model in action and ponder the
underlying message from the site, then give some thought to the
assumptions made in constructing the different apps and how this may limit
any conclusions made.
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Here are a few questions intended as prompts:
How does the app measure the percentage of alike neighbours? For
example consider a square near the centre of the large grid, see the
diagram below. By filling the surrounding spaces with either, squares,
triangles, or empty spaces, we arrive at the percentage of alike neighbours.
 Are all percentages possible?
 Explain your answer.
Consider how the possible values for the percentage of alike neighbours,
may change depending on the shape’s position. You could start by
examining a square in one of the corners of the large grid, for example (A)
in the diagram below. As you did in the previous example, work out all the
possible values for the percentage of alike neighbours. Now try a square
along one of the edges of the large grid for example (B). Compare the
possible percentages you have just obtained for (A) and (B), to the
percentages you previously obtained for a square in the central section (C)
A
C
B
Assume the simulation was run many times, with the same setting.
 Which of the three squares considered above (A, B, or C) , would you
expect to move more frequently on average?
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The screenshot below suggest that there is 56% segregation:
 How is this figure calculated?
 Is this a good way to measure segregation?
The initial problem starts with both shapes having the same requirements,
that is, that at least 1/3 of their neighbours need to be like them for them to
be happy.
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On the second app, shown in the screen shot below, you are allowed to
change this figure of 1/3 ≈ 33% to other values to investigate its effect on
the level of segregation. In the screenshot below the condition for moving is
set to “I’ll move if less than 50% of my neighbours are like me”
 Is there a maximum level you can set for this figure beyond which a
solution becomes impossible?
 Explain why.
 How about if the shapes showed different levels of preference, for
example would it be possible for a solution where squares required
75% to be alike, whilst triangles would be happy with 1/3?
 What constraint does this place on the settings?
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