Assignment 2

For this assignment, we used the “Segregation” model in Netlogo. This model studies how agents behave based on a percentage of similarity with their neighbors. Agents will demand anywhere from 0-100% of their neighbors are like them, or they will move until they are situated in such a way that their desires fit. Patterns emerge based on this need, and that’s what we’ve studied here.

 

 What minimum level of self-preference leads to emergent patterns of segregation?

Using the default number of agents (2000), I ran some tests to see the results.

The patterns that form are described in a later question.

With 2000 agents, neighborhoods begin to form around 60% until around 80% similarity wanted. These percentages correspond with how the code works: by looking at neighboring agents.

62.5% corresponds with 5/8 similar neighbors, and 75% corresponds with 6/8 similar neighbors.

These show in more detail how the confines of space affect the thresholds and why they occur so sharply. If the neighborhoods were more detailed, such as a group of 100 neighbors around an agent, I don’t think the thresholds of changes would be so sharp.

Once 7/8 neighbors must match (87.5%), the agents will never be “happy” and perpetually move, turning to the unstable state.

 

Does a specific threshold level exist that tips the system into an unstable state?

I decided to run some tests where I changed the number of agents (in increments of 100) and found the maximum percentages of similarity for each number of agents (in increments of ten) that resulted in all agents being happy. Because the model doesn’t behave the same way each time, it’s much like performing the experiment in the real world, and several trials are necessary to start to see the pattern. Anything above these numbers will tip the system into the unstable state of all agents never being 100% happy.

There were some sharp boundaries.

• With 500 agents, it was no problem to keep 100% happy because of the large “buffer zone”.
• By increasing the number of agents to 600, they would become unstable – and perpetually move – unless the similarity was reduced to 80%.
• As the number of agents increased, it was still possible to have 100% happy with 80% similarity, but the number of ticks required to “solve the puzzle” and end up with 100% happy agents increased – slowly at first, and then, before a “tipping point”, the number of ticks would increase a lot.
• The “tipping point” occurs when agents can no longer be 100% happy with the percentage of similarity selected, and end up moving forever.
• With a maximum number of agents of 2601, anything more than 2500 would result in so little buffer space that it was difficult for the agents to “move” and I ended the tests.

 

How does increasing levels of self-preference change the nature of segregation patterns that emerge?

The patterns that form depend on the number of agents (and therefore the amount of blank space) as well as the percent similar wanted. There are three distinct patterns. These patterns can be seen by the results as one increases the percentage of similarity wanted. Distinctions form in the data.

This example used 2000 agents, which had a moderate amount of empty space.

When agents wanted from 0 – 50% of their neighbors to be similar, agents go from not caring at all to wanting at least 4/8 neighbors to be similar. These are all easily achievable goals and few agents need to move for these things to happen. The pattern that occurs is “random noise”, because hardly any agents move away from the random starting position. Closer to 50% similarity, small neighborhoods form, but it is not the very noticeable neighborhoods that occur with higher similarity percentages.

When agents desire 5/8 – 6/8 of the neighbors to be similar, distinct neighborhoods form.

When agents desire 7/8 or more of the neighbors to be similar, the agents will never settle down and perpetually move, trying to fix the problem. The system is unstable.

 

What does the change in the unhappy-ratio at each time step tell you about the relationship between self-preference and the number of similar neighbors in one’s neighborhood?

The unhappy ratio decreases with each tick, because the agents moved based on their happiness – if they are unhappy, they move. The ratio is the percent unhappy over the percent similar, rounded to the nearest tenth. Here is an example of how it changed over one of the trials:

And a graph of its typical behavior if the system will result in 100% happy agents:

As the percent of unhappy agents goes down, the unhappy-ratio also goes down, and the percent similar rises. The happiness level is based on how many nearby neighbors are similar, and agents move if they are unhappy. Because the moving is random, the moving doesn’t always result in happier agents, but in simpler cases, it does. If agents are satisfied, they don’t move, so over time, the system grows happier, and the unhappiness ratio goes down.

 

What general conclusions can be drawn from your answers to (i) to (iii)?

The patterns that form depend on the number of agents (and therefore the amount of blank space) as well as the percent similar wanted. There are three distinct patterns:

1. The agents don’t really “care” about similarity, so none (or very few) move. The system is quickly “happy”, and no noticeable patterns emerge. It still looks very similar to the starting point, random “noise”.
2. The agents “care” enough about similarity to move, but are able to form neighborhoods of similarity rather quickly, which results in all agents being happy.
3. The agents “care” so much about similarity that they are perpetually moving, as no neighborhood configuration is possible for them to all be happy.