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Axelrod - Network

by Daniel Diermeier (Submitted: 06/01/2015)

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## WHAT IS IT?

This model simulates how people become similar through interaction. The idea is based on Robert Axelrod’s _Dissemination of Culture_ (1997). In his paper, Axelrod notes that one universal feature of culture is that it is "something people learn from each other" and makes two assumptions: 1) People are more likely to interact with similar people, and 2) people become more similar after interactions. He goes on to cite three principles upon which his study is based on: 1) Agent-based modeling, 2) no central authority, and 3) adaptive (as opposed to rational) agents.

## HOW IT WORKS

In this model, each agent has two properties: culture and similarity. Culture represents the distinctive characteristics of an agent, and similarity represents how similar its culture is to its linked neighbors. Culture is randomly assigned to each agent in the simulation, and similarity is determined by the amount of overlap in cultures between an agent and its neighbors. Users do not know the assigned cultures, but they can see how similar an agent is to its neighbors. In each tick, an agent potentially interacts with one of its linked neighbors. Interaction depends on the similarity between two agents; the more similar an agent is to its neighbor, the more likely they are to interact. If an agent does interact with its neighbor, then its own culture is modified to become more similar to its neighbor. If agents do not interact, then culture is unaffected.

## HOW TO USE IT

To start, select one of five setup versions. These versions differ in how the agents are connected to one another. The options are Lattice, Mean Field, Random, Scale Free, and Small World.

-Lattice: Creates cube-length^dimension agents and arranges and links them to represent a lattice.
-Mean Field: Creates N agents and connects every agent to every other agent.
-Random: Creates N agents. Each agent then randomly selects one other agent and makes a link with that agent. Though each agent may only select one target, it is possible for one agent to be the target of many other agents.
-Scale Free: Arranges N agents into preferential groups determined by the m0 and m variables.
-Small World: Creates N agents and arranges them in a circle. Each agent is linked with its adjacent agents.

When using the Lattice, Random, or Scale Free setup, the Layout button may be pushed to assist in visualization. Push Layout again to stop the agent rearrangement. The radial-central button may also be useful for visualization purposes.

Once the model is setup and you are ready to run the simulation, press the Go button. The simulation may be run simultaneously, on each tick every agent interacts with a neighbor, or not, on each tick one agent is randomly selected to interact with a neighbor. As the simulation runs, agents will change color from gray to various shades of blue. The darker the shade of blue, the more similar an agent is to its linked neighbors. The number of distinct cultures is tracked during this simulation. Press the Go button again to stop the simulation. Press the Recolor button to examine the distribution of culture. Each color represents a distinct culture. The resize button can help better see the color of the agents if they are too small.

## THINGS TO NOTICE

Notice the change in shades of blue as the simulation goes on; concurrently, notice how the number of distinct cultures changes. When pressing the Recolor button, notice the relation between same culture/color and linked agents.

## THINGS TO TRY

Adjust the five sliders under the variable section to play with larger or smaller network sizes. Adjusting the m and m0 sliders will also change the composition of the preferential groups used in the Scale Free setup.

## EXTENDING THE MODEL

Whether or not an agent interacts with its randomly selected neighbor depends on their level of similarity. The more similar two agents are, the more likely they are to interact, and thus adjust the interactor's culture. By changing the interaction rule, one may examine how culture changes when agents are more or less likely to interact with those they are dissimilar too. This may be examined by adjusting the go function under the UPDATE RULES section of the code.

Additional setup procedures may also be coded and tested under this Axelrod model.

Under the current modeling choice, only the interactor changes its culture, the interactee is not affected by interaction. One potential extension is to have only the interactee change its culture, or to have both agents adjust their culture after interaction.

It may be interesting to test how the simulation runs if there are agents who never adjust their culture mixed in with those who do. It may also be interesting to model situations where two agents have asymmetric likelihoods of culture-changing interactions between themselves, e.g. for fixed similarity, agent A is more likely to adjust its culture after interacting with agent B than agent B is after interacting with agent A.

## RELATED MODELS

Confident Voter
Heterogeneous Voter
Social Consensus
Ising
Potts
Turnout

## CREDITS AND REFERENCES

Axelrod, Robert. 1997. "The Dissemination of Culture: A Model with Local Convergence and Global Polarization." _Journal of Conflict Resolution_ 41 (2): 203-26.

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