Dynamic Stability of the Replicator Equation with Continuous Strategy Space

We extend previous work that analyzes the stability of dynamics on probability over continuous strategy spaces. the stability concept considered is that of convergence to the equilibrium distribution in the strong topology for all initial distributions whose support is close to this equilibrium. Stability criteria involving strategy domination and local superiority are developed for equilibrium distributions that are monomorphic (i.e. the equilibrium consists of a single strategy) and for equilibrium distributions that have finite support.