We consider processes in which norms of behavior are transmitted through social or geographic networks. Agents adopt behaviors based on a combination of their inherent payoff and their local popularity (the number of neighbors who have adopted them) subject to some random error. Extending work of Blume (1993,1995), Ellison (1993), and Morris (1997), we characterize the long-run dynamics of such processes in terms of the geometry of the network, but without placing a priori restriction on the network structure. We show first that the relative likelihood of different states can be described in terms of a potential function that is inversely related to the length of the boundary between regions where norms behavior differ. As in a variety of other evolutionary models, the most likely state is the one in which everyone is coordinated on the risk-dominant equilibrium. We then show that, if agents interact in sufficiently small, close-knit groups, the expected waiting time until almost everyone is playing the risk-dominant equilibrium is bounded above independently of the number of agents and independently of the initial state. Simulation results indicate that convergence is surprisingly rapid even in very large networks, provided they are close-knit.
The working papers represent drafts that have been internally reviewed but are not official publications of the Institution.