variations among individuals—you need game theory to tell you what happens when those individuals interact.

SOCIOPHYSICS AND GAME THEORY

After all, when you get to really complex social behaviors—not just yes or no votes, but the whole spectrum of human cultural behavior and all its variations—the complex interactions between individuals really do matter. It is yet again similar to the situation with molecules in a gas. In his original math describing gas molecules, Maxwell considered their only interaction to be bouncing off of each other (or the container’s walls), altering their direction and velocity. But atoms and molecules can interact in more complicated ways. Electrical forces can exert an attractive or repulsive force between molecules, and including those forces in the calculations can make statistical mechanical predictions more accurate.

Similarly, the behavior of people depends on how they are affected by what other people are doing, and that’s what game theory is supposed to be able to describe. “Game theory was created,” Colin Camerer points out, “to provide a mathematical language for describing social interaction.”10 Numerous efforts have been made to apply game theory in just that way. One particularly popular game for analyzing social interaction is the minority game, based on an economist’s observations about a Santa Fe bar.

Keep in mind that in game theory, a player’s choices should depend on what the other players are choosing. So the game as a whole reflects collective behavior, possibly described by a Nash equilibrium. In simple sociophysics models based on neighbors interacting, the global collective behavior results from purely local influences. But the Nash equilibrium idea suggests that individual behavior should be influenced by the totality of all the other behaviors. It may be, for instance, that the average choices of all the other players is the most important influence on any one individual’s choice (in physics terms, that would correspond to a “mean-field theory” version of statistical mechanics).

In traditional game theory, each player supposedly is 100 per-



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