Type interaction models and the rule of six

Abstract

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.