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Axelrod_Cultural_Dissemination

by Arezky H. Rodríguez (Submitted: 03/14/2013)

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## WHAT IS IT?

This is Axelrod’s model of cultural dissemination. See Reference at the end. It is an agent-model designed to investigate the dissemination of culture among interacting agents on a society.

Axelrod model consists in a population of agents, each one occupying a single node of a square network of size L. The culture of an agent is described by a vector of F integer variables called 'features'. Each feature can assume q different values between 0 and q-1. In the original Axelrod model the interaction topology is regular bounded (non-toroidal). Each agent can interact only with its four neighbors (von Neumann neighborhood).

Dynamics are based on two main mechanisms: (1) agents tend to chose culturally similar neighbors as interaction partners (homophily) and (2) 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 (multicultural society). 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).

## HOW IT WORKS

Each agent is located at each patch of the grid with the default shape. Agents hold a number of features F. Each feature is a nominal variable that can adopt a certain number of values (called traits) from 0 to q - 1. Initially, agents adopt randomly chosen traits. At each time step (tick) agents update its cultural value in an asyncronous-random updating. That is that the computer makes a list where all agents are included in a random order and the list is followed until all agents are choosen. Each agent them become a focal agent and then, one of the focal agent’s neighbors is selected at random. Neighbor agents are those who are in distance less than the value of the parameter 'radius'. If radius = 1, then it is von Neumann neighborhood. 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 agent until the list is exhausted and it follows the next time step (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 selecting the size of the grid society on x and y directions and write these values on 'world-size-x' and 'world-size-y'. Also you should choose value for F (number of features), q (how many traitseach feature cand adopt) and radius (size of the neighborhood). Here, 1 means that each agent has 4 neighbors, 2 corresponds to 12 neighbors, and so on.

Each agent adopts a color which represents its culture. If two agents adopt the same color, they have the same culture.

Click on Go and the simulation starts. You can follow the changes of the agents culture according to his color. Furthermore, there is a graph reporting the number of different cultures on the society and the number of possible and real interactions. A possible interaction is that which agents share more than zero and left than all its features. A real interaction is when focal agent actualy change the value of one of its features.

Simulation stops when the number of possible interactions reaches zero. That means that each agent share all of none of its traits value with all its neighbors.

At the end it is calculated and reported the number of cultural regions in the population and the number of agents in the biggest one (also normalized). A region is a set of agents that are similar on all features. You can choose to save these values with 'saving? on'.

We included an extensions of Axelrod’s model: agents can move.
Then, you should also decide if the agents can move or not. In original Axelrod model the agents do not move. If moving, select the velocity of agent movement with 'veloc', select the length of the step with 'steplength' and the angle of rotating with 'angle'. If moving, at each tick agents decide to move taking 'veloc' as a probability. In case of actual movement, agents select at random an angle were the upper half values add this angle value to the current one the agent has and the lower half subtracts this angle to the current one. Then, ones direction is selected, agent moves a distance 'steplength'.

## THINGS TO NOTICE

Here we have setted toroidal boundaries, but the simulation can properly function as well in the original non-toroidal one. In our case, the four von Neumann neighbors are at distance 'radius' one. The model permits to change the value of 'radius' to explore the implications of other neighborhood sizes. It is also implemented the possiblity for agents to move.

At the end, in the absorving final state, when calculating for the number of regions, the model makes different visible networks which include all neighbors agents with the same culture. Then, when counting the number of cultural domains it is considered that two domains are different if they are not connected, even if agents in both domains share same culture.

Note also that two agents could have similar (but with zero overlap) cultural values and then, its corresponding colors could be so similar that it could induce to think that the cultural values are the same. Just check to see that it is not.

## THINGS TO TRY

Vary the population size, the number of features, the number of traits, the range of interactions and also the movement of the agents. The program stops when the first absorving state is found (the number of possible interactions are zero on one time step), even if the agents are moving. Try toroidal and not toroidal borders activating ‘World wraps horizontally’ and ‘World wraps vertically’ in the Settings menu.

## EXTENDING THE MODEL

Many many extensions of this model have been proposed (see e.g. references below). One of the most interesting is certainly the inclusion of 'social influence' instead of dyadic interaction (see e.g. references below). It has been shown that this makes the persistence of different cultural region very strongh.

## RELATED MODELS

There are a lot of related models. You can follow the References here after or in the literature.

## CREDITS AND REFERENCES

This model has been developed by Robert Axelrod.
It was implemented by Arezky H. Rodríguez (arezky@gmail.com).

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. 2008. “Local Convergence and Global Diversity: From Interpersonal to Social Influence.” arXiv:0808.2710 [physics.soc-ph].

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. 2003. “Global culture: A noise-induced transition in finite systems.” Phys. Rev. E 67, 045101.

Klemm, K., V. M. Eguiluz, R. Toral, and M. San Miguel. 2003. “Nonequilibrium transitions in complex networks: A model of social interaction.” Phys. Rev. E 67, 026120.

Copyright 2013 by Arezky H. Rodríguez (arezky@gmail.com). All rights reserved.

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