Thomas Schelling demonstrated how a series of individual choices based on mild preferences can lead to racial segregation. He used nickles and dimes on a board. Every coin made a decision to move on the space based on its order of preferences. Dimes wanted at least one dime as a neighbor, and nickels wanted at least one nickle neighbor. Even if Dimes only has a slight preference for dimes over nickles, over time, dimes and nickles would segregate.

Political violence intensifies group preference. This leads to faster segregation with stronger avoidance behavior. Patriotism is a mutual defensive pact, afterall.

Take Group A and Group B.
If A moves near another A, A gets a 0.6 utility
If A moves near B, A gets a 0.4 utility.

A rationally chooses the slight utility of moving near A over B. Over several moves, A quickly cluster together leaving B’s to cluster by themselves.

The grows more complicated if you throw in additional variables. Here’s a set of programs to model segregation behavior. Notes and explanations here.

Take Red, Green, and Blue individual actors and mix them randomly over space. They prefer to cluster together in groups of a certain size and in an order of preference. Blue prefers Blue, then Green, then Red. And so on for the rest As the game progresses, we see the segregated communities form with certain patterns. Over variables (like business interests) prevent a perfect cluster. Blues may still deal with Reds in business, because the net utility outwieghs racial preference.

Civil Wars reorder individual preferences. Red, Blue and Green lose utility for any intergroup interaction. Red gets a high utility from killing blue, so Blue gets utility from avoiding Red. This creates extremely tight clusters – if guarded, these clusters become safe havens.

Segregation provides protection. Visualize equal numbers of Red and Blue agents. They are mildly segregated by movement preference, but there are economic interests between them. Red and Blue go to war, each agent has a 50% probability of killing another agent if they fight. A few Blue businessmen live in Red neighborhoods and vice versa. They are quickly isolated and eliminated (5 Red Agents swarm 1 Blue Agent – there is overwhelming probability of killing him). Blue Agents are safer in Blue neighborhoods because of mass. If 5 nearby Red Agents approach a Blue neighborhood, they are repelled by 8 Blue agents. Both sides can reach an equilibrium where any agent cannot approach the other agent’s neighborhoods without worsening his probability of survival.

There are ways of changing the mechanics of the game. We can give weapons to Red and disarm Blue to increase the probability of a Red Agent killing a Blue Agent. Blue Agents have to attack with 2-1 odds to have a favorable chance of winning. This can lead to Red Agents penetrating the Blue neighborhood over time. Arming Blue and reinforcing their numbers again restores equilibrium.

This can be helpful in understanding the principles of riot control and ethnic genocide.