Freely forming groups: Trying to be rare

Abstract

A simple weakly frequency dependent model for the dynamics of a population with a finite number of types is proposed, based upon an advantage of being rare. In the infinite population limit, this model gives rise to a non-smooth dynamical system that reaches its globally stable equilibrium in finite time. This dynamical system is sufficiently simple to permit an explicit solution, built piecewise from solutions of the logistic equation in continuous time. It displays an interesting tree-like structure of coalescing components.2000 Mathematics subject classification: primary 92D25, 91A40; secondary 34A36, 34A05, 34D20.