Social Networks and the Convergence of Population Attributes: A Generalization

Analysis of social interactions has recently become an important area of economic research, and the focus of researchers in this area has increasingly shifted toward dynamic models. In one recent contribution, Brueckner and Smirnov (2006) analyze the evolution of population attributes in an exceedingly simple model where an agent’s attributes at time t are equal to the average attribute value among his acquaintances. The pattern of acquaintances in the population is determined by the social network, and Brueckner and Smirnov (BS) explore the effect of network characteristics on the convergence of population attributes over time. They show that some simple sufficient conditions on the network structure ensure convergence to a "melting-pot" equilibrium, where attributes are uniform across agents. The present paper provides a generalization of BS’s analysis, allowing for a more general form of the rule governing the evolution of population attributes. The analysis shows that BS’s previous conclusions continue to hold under this generalization, while also providing a result that can be applied more generally to other models.