Type interaction models and the rule of six

In this paper, I describe and analyze a class of type interaction models. In these models, an infinite population of agents with discrete types interact in groups of fixed size and possibly change their types as a function of those interactions. I then derive conditions for these models to produce multiple equilibria. These conditions demonstrate a trade off between the number of types and the size of the interacting groups. For deterministic interaction rules, I derive the rule of six: the number of agent types plus the group size must be at least six in order to support multiple equilibria given a spanning assumption.Troy Tassier provided help with early versions of this model. Ken Arrow, Bob Axelrod, Larry Blume, Steven Durlauf, David Harris, John Holland, Lu Hong, Mercedes Pascual, Rick Riolo, and Carl Simon provided input on earlier drafts of this research. Financial support from the National Science Foundation, the James S. McDonnell Foundation and the John D. and Catherine T. MacArthur Foundation is gratefully acknowledged.