Basins of Attraction, Long Run Equilibria, and the Speed of Step-by- Step Evolution.

The paper provides a general analysis of the types of models with E-Perturbations which have been used recently to discuss the evolution of social conventions. Two new measures of the size and structure of the basins of attraction of dynamic systems, the radius and coradius, are introduced in order to bound the speed with which evolution occurs. The main theorem uses these measures to provide a characterization useful for determining long run equilibria and rates of convergence.