Game theory and segregation

Would you rather live is a neighborhood where everyone shares your skin color?

Most people would say that they are not racist and would prefer to live in a mixed neighborhood. If this is the case then why are most neighborhoods segregated?

Thomas Schelling analyzed this problem using game theory and showed that even if people are not racist you can still end up with segregated neighborhoods.

We will assume that everyone is happy in a mixed neighborhood but doesn’t want to be in an area where they are in a small minority. (To simplify things we will assume that people are either black or white, obviously this isn’t the case but it makes things easier to explain)

If we start with a random mix of people then there will be some mixed areas where everyone is happy but there will also be areas which, just through chance, start with a majority of black people and other areas where there is a majority of white people.

In the areas which start off with a majority of black people there will be a few white people who would be happy in a mixed neighborhood but don’t want to be in a small minority in an area. These people will then be more likely to move out to another area. When they move out the area ends up with a higher proportion of blacks. The opposite happens in areas which start with a majority of white people: the black people who are in a minority move out which means the area ends up with a high proportion of whites.

After this is repeated a few times we end up with highly segregated neighborhoods even though everyone would have been happy in a mixed neighborhood. All it took to reach this state was a small preference to avoid being in a minority, people weren’t racist and everyone was happy to be in a mixed neighborhood but we ended up with segregation anyway.

To see a model of how this works check out this link to NetLogo. It generates a random mixture of red and green at the start and you can see that this quickly moves to be a highly segregated population.

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