Topologies Of Social Interactions

We examine in this paper the role of an economy's social interaction structure, defined as a graph. Individuals care about the decisions of their neighbors. We extend the behavioral discrete-response rules along the lines of the interactive discrete choice model of Brock and Durlauf (2001) to static and dynamic settings and also explore properties of a richer class of {\em anisotropic} equilibria in the context of richer social interaction topologies, such as circular interaction and one-dimensional lattice. We examine the model where individuals make decisions on the basis of observations on the actual decisions of their neighbors in a static setting and explored some of the issues that come up in dynamic settings. In the static case, we accomplish this by exploiting the properties of Markov random fields as Gibbs states. We also link interactive discrete choice models with the econometric theory of simultaneous systems of equations modelling discrete decisions. We examine the role of closure in social structure. With local interaction either in the form of circular or of interaction along a line, synergistic effects lead to spatial oscillations and clustering, with the ``most unstable'' states pushing the economy away from the symmetric isotropic outcome, which is unstable. We obtain general results for the dynamics of adjustment towards isotropic equilibria and shows that they combine spectral properties of the adjacency matrix with those associated with the nonlinearity of the reaction functions that lead to multiplicity of steady states. When all agents have the same number of neighbors the dynamics of adjustment exhibit relative persistence. Cyclical interaction is associated with endogenous and generally transient spatial oscillations that take the form of islands of conformity. The paper also examines stochastic dynamics for general interaction topologies. Yannis M. Ioannides Department of Economics Tufts University Medford, MA 02155 Voice: 617 627 3294 Fax: 617 627 3917 yannis.ioannides@tufts.edu www.tufts.edu/~yioannid