Topologies of Social Interactions

The paper adapts to richer social structures the Brock-Durlauf model of interactive discrete choice, where individuals’ decisions are influenced by the decisions of others. Social structure is modelled by a description of who interacts with whom, by means of a graph, with individuals as vertices and interaction between individuals as edges. The paper extends the mean field case to such alternative stylized interaction topologies as when individuals are connected through a common intermediary, the graph topology of interactions is a cycle or an one-dimensional lattice. Some results are qualitatively similar to the mean field case, but a richer class of anisotropic equilibria is also explored, for the case of the cycle and one-dimensional lattice. Social equilibria are also explored under the condition that individuals’ behavior is affected by the actual behavior of their neighbors and links are made with the econometric theory of systems of simultaneous equations modelling discrete decisions. The paper studies the role of interaction topology for the dynamics of adjustment towards isotropic equilibria. It compares circular interaction along a one-dimensional lattice with and without closure and shows that both lead to endogenous and generally transient spatial oscillations. However, closure of the social structure is responsible for relative persistence.interactions, dynamics, spatial oscillations, interactive discrete choice, neighborhood effects, Ising model, random fields