Charismatic leaders and media personalities can be destabilizing influences on social groups, according to various "small-world network" models. This conclusion that seems intuitively consistent with historical events such as civil uprisings and religious movements.

But, surprisingly, long range connections in a network
(which reduce the degree of separation among members) seem to hinder the system's return to equilibrium, according to a new model that combines small-world scenarios with a version of the "prisoner's-dilemma" proposition, according to which a pair of captured criminals ponder strategy: if neither criminal confesses, both go free; if one confesses, the other receives a stiff sentence; if both confess, they each receive moderate sentences. The study may help us to understand the dynamics of such social behaviors as smoking among teenagers, which is influenced by various factors including local social surroundings and the examples set by media role models.

A collaboration of researchers from Ajou University, Chungbuk National University, and Seoul University in Korea, and Umea University in Sweden recently discovered the instability introduced to social systems by influential persons in a simplified, two-dimensional, small world network.

The researchers (Beom Jun Kim, eomjun@ajou.ac.kr">beomjun@ajou.ac.kr, 82-31-219-2571) created a 1024-element grid of points that represented an interconnected group of individuals. Some points in the grid were randomly designated to be cooperators (e.g., nonsmokers), and others were designated to be defectors (e.g., smokers). Once the grid was established, the individuals began playing a version of the prisoner's dilemma game with their eight nearest neighbors.

The classic prisoner's dilemma is a game involving two players who each decide whether or not to cooperate with authorities in efforts to minimize their own prison sentences. In the new small-world/prisoner's-dilemma model, each individual surveys his nearest neighbors and scores points depending on their own status as a cooperator or a defector, and the statuses of their neighbors. The individuals may then change their status based on their score after each round of the game.

To model the effect of an unusually powerful individual, the researchers made connections from a single influential member to several distant network members. In real life, for instance, the influential member might represent a celebrity or religious demagogue with access to the media or the Internet. When the influential member was a defector, the network collapsed into a numerical kind of anarchy, with many cooperators defecting as well.

Eventually, the benefits of cooperating return the system to equilibrium, but the more long range connections in the network, the slower the system's recovery. Although the model is clearly a crude reflection of human interactions, it suggests that increasing numbers of long range connections between people may help destabilize communities. The result is in contrast to the general perception that connections across cultures and nations is exclusively beneficial to society. (B.J. Kim et al., Phys. Rev. E, August 2002)