Dynamics in stochastic evolutionary models

First published: 01 February 2016 We characterize transitions between stochastically stable states and relative ergodic probabilities in the theory of the evolution of conventions. We give an application to the fall of hegemonies in the evolutionary theory of institutions and conflict, and illustrate the theory with the fall of the Qing dynasty and the rise of communism in China. We are especially indebted to Juan Block for his many comments and suggestions. We would also like to thank Drew Fudenberg, Kevin Hasker, Matt Jackson, Peyton Young, and five anonymous referees. We are grateful to NSF Grant SES-08-51315 and to the MIUR PRIN 20103S5RN3 for financial support.