Unpublished,
Diffusion in Social Networks
(1999)Center on Social and Economic Dynamics.
Abstract
We consider processes in which norms of mehavior are transmitted through social or geographic networks. Agents adopt behaviors based on a combination of their inherent payoff anf 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 characerize the long-run dynamics of such processes in terms of the geometry of of the network, but without placing a priority 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 shere norms of behaviour differ. As in a variety of other evolutionnary 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 equilbrium 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.
