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Robert Axelrod, Dec. 22, 1995

Potential Extensions of Axelrod's Culture Model

This is a more detailed version of the section on "Extensions of the Model" from Axelrod, ""An Agent-Based Model of Social Influence."

* Cultural Drift.

In the basic model, a value of a particular cultural feature changes only through adopting a neighbor's value in an interaction. Cultural drift could be added as a process of spontaneous change in a feature's value at a site, akin to mutation in genetics. Presumably, the effect would be to allow boundaries between cultural regions to "dissolve" and therefore would promote the eventual homogenization of culture. in the standard model, once all cultural distances are zero or maximal, there can be no further change because all pairs of neighbors would be either identical or incompatible. With cultural drift, however, even if two adjacent sites are incompatible one of them can spontaneously change and then start interacting with the other. This means that even a boundary between distinct cultural regions can erode, and eventually the regions might merge. Ironically, drift promote homogeneity by preventing permanent incompatibility. On the other hand, cultural drift can break up a cultural region that has formed. So its impact could be subtle and interesting.

* Structured Initial Conditions.

The initial values of cultural features are assigned at random in the basic model. A wide variety of interesting experiments could be conducted by having some or all of the features given particular values. For example, suppose one wanted to study the effects of the seemingly universal phenomena that "things are different in the south." An easy way to do this would be to give one or two of the cultural features one value in the northern sites, and a different value in the southern sites. Would regions tend to form based on these small initial differences? If so would the eventual boundary between the regions closely correspond to the initial line between the north and the south? Another example of an interesting experiment would be to see how easy or hard it is for an initial advantage in numbers to take over a territory. A simple way to study this is by giving a slight bias in the original assignment of values to features throughout the territory, and seeing how much bias it takes to overcome the tendency to get swamped by random variations, and eventually to dominate the entire territory.

* Terrain.

In the basic model, each of the neighbors of a chosen site has an equal chance of being tested for a possible interaction. Suppose there is a mountain range down the middle of the map, so that contacts are less likely between adjacent sites on opposite sides. Presumably, boundaries between emerging cultural regions would tend to coincide with such impediments to interaction. But just how much of an impediment does a terrain feature have to be in order for it to shape cultural boundaries? Is the equivalent of a foothill enough to show up on a cultural map? Conversely, if a terrain feature such as a river slightly favors interaction between adjacent (or even distant) sites, does this tend to prevent cultural boundaries and promote regions of shared culture? If so, just how much help does the favorable terrain have to generate a cultural region?

* Status.

Low status groups are more likely to adopt things from high status groups than vice versa. This can be modeled by assigning status to each site, either randomly or in some geographically structured manner. An interaction between sites of different status would tend to cause the lower status site to adopt part the culture from the higher status site. Would the initial values of the high status sites tend to dominate the entire territory, even though such sites were few and far between?

* Cultural Attractiveness

Some cultural features might be favored in the adoption process over others. For example, if Arabic numbers are more likely to be adopted by people using Roman numerals than the other way around. Just as status modifies the likelihood of any features being copied, the attractiveness of a particular cultural feature can affect the chance that it will be adopted or dropped in an interaction. This differential attractiveness of cultural features might be due to superior technology (as in the case of number systems), or it might be due to seemingly arbitrary preferences (as the refinement of esthetic tastes). One way to model this would be to favor higher values of a given cultural feature over lower values. To be concrete, consider the original example from Table 1 in which an interaction between site A and its neighbor to the south led to a transfer of culture on the first feature from the neighbor to site A, changing its culture from 82330 to 62330. If higher values were assumed to be more attractive, then it would be more likely that the neighbor would be the one to change its first cultural feature, adopting A's value of 8 to replace its own value of 6. Presumably, features that are culturally attractive would tend to drive out less attractive features. But just how attractive does a feature have to be to dominate? And does the process of differential attractiveness tend to lead to larger (and thus fewer) regions?

* Technological Change.

When technology advances, new and possibly more attractive values are introduced as possible types for a given cultural feature. This is easy to model by starting with only a few low values, and then gradually introducing higher (and thus more attractive) values. This would allow the study of the spread of standards, such as QWERTY keyboard and VHS video standards (see Lane 1985). The present model has no explicit economies of scale, as are common in standards setting cases. Nevertheless, as discussed earlier, large regions do tend to "eat" small ones. The revised model could address the question of when a less attractive technology can survive and even flourish as a function of its ability to get established first.

* Material Basis of Culture.

The cultures of herders and farmers tend to differ, in part because what works well in the hills does not work well in the plains and vice versa. Such differences provide a material basis for culture. The extent to which observed cultural differences can be attributed to such material differences rather than random factors is a major question in anthropology. The basic model could be extended to study this question by assigning terrain to sites, and then supposing that there were one or more features whose attractiveness depended upon the site's terrain. For example, low values on the a cultural feature might be more attractive in the plains, and high values were more attractive in hills. Just how strong would this tendency have to be for the emerging cultural boundaries to correspond closely to the terrain?

* Broadcasting

So far, the cultural change model has studied only local interactions. The model could be expanded to study the effects of mass communication, such as printed books, and television. Mass communication, whether political controlled or not, has had a great influence on the formation of common languages and indirectly supports the formation of nation states (Deutsch 1953, Anderson 1991). With mass media, many people are exposed not only to the cultural features of their neighbors, but also to specific messages that are widely disseminated. This is easy to add to the model by supposing that some proportion of each site's interactions are with a specific common culture message that is being transmitted to everyone. How effective would such a transmitted culture be in promoting homogeneity in the face of local heterogeneity?

* Cultural Packages.

Doing things one way is sometimes effective only if you are also doing other things in a certain way. For example, certain cultural practices work effectively together but lose their meaning and effectiveness if undertaken in isolation. One way this can be incorporated into the model is by saying that a value of a cultural feature is attractive only if it matches a certain value on another cultural feature. The question then arises whether cultural packages are able to spread as efficiently as single cultural features.

* Long distance interaction.

The basic model has already been used to study the effects of expand the range of interactions from four to twelve nearby sites. An interesting possibility to explore is the effect of interactions at large geographic distances. There are many ways of doing this.

a. Complete mixing would suppose that everyone is a neighbor of everyone else. This is would eliminate the effect of geographic distance altogether. It would presumably tend to promote homogeneity of culture. But even with just the convergence mechanism of the basic model, it would still be possible for two or more distinct cultures to be stable provided that each of them had no cultural features in common with any of the others.

b. A less drastic method of expanding neighborhoods would be to suppose that for a given site, the probability of trying to interact with another site falls off with the geographic distance between them (see Carrothers, Gerald A.P.,1969. "An historical review of the gravity and potential concepts of human interaction, in Ambrose, Peter (ed.), Analytic Human Geography New York.) For example, there could be 50% chance of interacting with an adjacent site, a 25% chance of interacting with a site adjacent to one of the immediately adjacent sites, and so on.

c. Still another approach is to study the effects of allowing only a few specialist sites to engage in long distance interaction.

d. Finally, one could suppose that some or all of the actors in the model are allowed to migrate, rather than be confined to fixed sites. This would allow the analysis of assimilation of newcomers into within an area that had a more or less uniform cultural. Under what conditions do the newcomers get totally absorbed? How and when is the established culture affected by the newcomers?

* Organizational Culture.

Organizations have culture too. In organizations, people interact with each other in ways that are structured by location in the organization, rather than geographic location. This is easy to model by assuming the neighborhood of a typical worker is that worker's boss, the other subordinates of the worker's boss, and the subordinates of that worker. For example, if every manager had three subordinates, then everyone (except the top boss and the lowest workers) has six neighbors: one boss, two peers, and three subordinates. The top boss has three neighbors (the subordinates), and the lowest workers also have three neighbors (one boss and two peers). It is not clear whether this hierarchical structure would tend to converge more or less completely and quickly than the geographic neighborhood structure of the basic model. One could go further, and generalize neighborhoods to any arbitrary network of connections between individuals. This would allow an analysis of the effects of multiple roles as people interact with colleagues at work, relatives and neighbors at home, and friends at leisure.

* Sociology of science.

Sociology of science studies how discovery and innovation spread within and between semi-isolated disciplines. This process could be systematically analyzed by combining the mechanisms of cultural drift, technological change and organizational culture discussed above.[1]

* Cultural Divergence.

It is a truism that when two people of quite different cultures meet, they may tend to exaggerate their differences rather than assimilate to each other. The basic model assumes that an interaction between two sites can only cause convergence of their cultures. This was a deliberate choice to see just how much the simplest version of the model can do. Even the simplest model can generate divergence since when a site converges toward one of its neighbor sit may well be diverging from other neighbors. Moreover, the basic model displays a tendency for distinct cultural regions to form which have nothing in common with each other. One could go further, however, and add to the basic model a mechanism that required interactions between two sites to make their cultures diverge under some circumstances. An interesting mechanism to explore is that the probability of two sites diverging in proportional to their cultural distance. This is exactly analogous to the original process of the probability of convergence being proportional to cultural similarity. The first question is what happens when only divergent interactions are allowed. The second question is what happens when both convergent and divergent interactions are allowed. Presumably, adding divergent interactions to the basic model will cause distinct regions to develop in greater numbers and become stable in less time.

[1]I thank Robert Pahre for this suggestion.

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