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AxelrodV2

by MIchael Maes and Sergi Lozano (Submitted: 11/05/2008)

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WHAT IS IT?

This is Axelrod's model of cultural dissemination. It models a population of actors that hold a number of cultural attributes (called features) and interact with their neighbors. Dynamics are based on two main mechanisms. First, agents tend to chose culturally similar neighbors as interaction partners (homophily). Second, during interaction agents influence each other in a way that they become more similar. The interplay of these mechanisms either leads to cultural homogeneity (all agents are perfectly similar) or the development of culturally distinct regions. The model allows studying to which degree the likelihood of these two outcomes depends on the size of the population, the number of features the agents hold, the number of traits (values) each feature can adopt and the neighborhood size (interaction range). We furthermore implemented cultural mutation and random interaction.

HOW IT WORKS

Each patch of the grid represents an agent. Agents hold a number of features. Each feature is a nominal variable that can adopt a certain number of values (called traits). Initially, agents adopt randomly chosen traits.
During each tick, the computer randomly selects a patch as the focal agent. Then, one of the focal agent's neighbors is selected at random and the cultural overlap between these two agents is computed. The cultural overlap is equal to the percentage of similar features.
With probability similar to the overlap, the two agents interact. Otherwise, the program continues with the next tick. An interaction consists of selecting at random one of the features on which the two agents differ and changing the focal agent's feature to the interaction partner's trait.
Note that if the overlap is zero, interaction is not possible and the respective agents refuse to influence each other.

HOW TO USE IT

First, you should choose the population size. Use the black arrows in the grid window to manipulate the size of the grid.
Second, click on SETUP to initialize the population. You can influence, how many features the agents hold by using the 'NUMBER_OF_FEATURES' slider. How many traits each feature can adopt can be changed with the 'NUMBER_OF_TRAITS' slider. Furthermore, you can vary the size of the neighborhood. Here, 1 means that each agent has 4 neighbors. 2 corresponds to 8 neighbors and 3 to 12 neighbors. In the grid, each patch (agent) adopts a color which represents the agent’s trait on the first feature. If two patches adopt the same color, they are similar on the first feature.

Click on RUN and the simulation starts. You can follow the changes of the first feature in the grid. Furthermore, there is a graph reporting the number of cultural regions in the population. A region is a set of agents that are similar on all features

We included two crucial extensions of Axelrod's model. First, you can implement cultural mutation, meaning that sometimes the computer changes a randomly chosen feature of a randomly chosen agent to a randomly chosen trait. The probability of such changes can be influenced using the 'MUTATION_RATE' slider.

Secondly, we allowed for interaction between dissimilar neighbors. In the original model, agents do not interact when the overlap is zero. It has been shown (see references below) that relaxing this assumption changes the outcomes of the model significantly. We implemented that as follows. If two agents that are dissimilar on all features are selected for interaction, then the probability that social influence occurs is similar to the value chosen with the 'RANDOM_INTERACTION' slider.

THINGS TO NOTICE

Note that the model does not stop 'ticking' when equilibrium is reached. When there are no changes in the grid and the number of regions is stable over a reasonable long time, you should click on the RUN button to stop the process.

Note furthermore that for the assessment of the number of regions, the model only counts the number of distinct attribute vectors in the population. The program does not check if two sets of agents that hold similar features are connected or not. It could thus happen that you see for instance three regions in the grid but the number of regions is only 2.

You can use the 'REPORT_CC' switch to follow the steps of the simulation and for debugging. Note that this makes the program slower.

THINGS TO TRY

Vary the population size, the number of features, the number of traits and the range of interactions. Conduct experiments to find out under which conditions the model predicts cultural differences. You will find quite some counter intuitive effects. Axelrod’s paper (see below) provides you with explanations for these effects.

In addition, you could change grid to a torus (a world that looks like a donut) by activating 'World wraps horizontally' and 'World wraps vertically' in the Settings menu. Why do the model's implications change?

Experiment with a very small mutation rate. What happens? Why? Try also high mutation rates.

Allow for random interaction. To start with, you could run a simulation without random interaction until stable regions have developed and then put the 'RANDOM_INTERACTION' slider to 5% and click on run again.

EXTENDING THE MODEL

Many extensions of this model have been proposed (see e.g. references below). One of the most interesting is certainly the inclusion of metric features. Interestingly, it has been shown that this makes the persistence of different cultural regions very unlikely. Try to think of ways to make cultural diversity possible again.

Incorporate social networks into this model. Currently, agents interact only with their neighbors and all agents (except those at the borders) have the same number of neighbors. Both could be changed.

NETLOGO FEATURES

Note that the agents (patches) hold several features. We used lists to implement that.
The model allows varying the size of the neighborhoods.

RELATED MODELS

Flache, Andreas, and Michael Mäs. 2008. "How to get the timing right? A computational model of how demographic faultlines undermine team performance and how the right timing of contacts can solve the problem." Computational and Mathematical Organization Theory 14:23-51.

Hegselmann, Rainer, and Ulrich Krause. 2002. "Opinion Dynamics and Bounded Confidence Models, Analysis, and Simulation." Journal of Artificial Societies and Social Simulation 5.

CREDITS AND REFERENCES

This model has been developed by Robert Axelrod. It was implemented by Sergi Lozano (slozano@ethz.ch) and Michael Maes (m.maes@rug.nl).

This is the paper where Axelrod presented the model:

Axelrod, R. 1997. "The dissemination of culture - A model with local convergence and global polarization." Journal of Conflict Resolution 41:203-226.

Extensions can be found at:

Flache, A., and M. Macy. 2006. "What sustains cultural diversity and what undermines it? Axelrod and beyond." arXiv:physics/0604201v1 [physics.soc-ph].

Flache, A., and M. Macy. 2007. "Local Convergence and Global Diversity: The Robustness of Cultural Homophily." arXiv:physics/0701333v1 [physics.soc-ph].

Klemm, K., V. M. Eguiluz, R. Toral, and M. S. Miguel. 2003a. "Global culture: A noise-induced transition in finite systems." Physical Review E 67:-.

Klemm, K., V. M. Eguiluz, R. Toral, and M. San Miguel. 2003b. "Nonequilibrium transitions in complex networks: A model of social interaction." Physical Review E 67

Copyright 2008 by Sergi Lozano (slozano@ethz.ch) and Michael Maes (m.maes@rug.nl). All rights reserved.

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