Higher Order Information Complementarities and Polarization

I study endogenous network formation in an environment in which individuals want to forecast a stochastic state and it is costly for them to communicate with others to exchange some exogenously observed information. Due to the existence of information complementarities, individuals’ preferences for networks in which they have multiple neighbors cannot be characterized by a linear ranking of the pairwise correlations between their signals. Instead, these complementarities generate a counterintuitive result: for a fixed number of individuals, information structures exist in which all signals are conditionally positively correlated, and these are preferred to a structure in which all signals are conditionally independent. Therefore, it may be that the only strongly stable network consists of two cliques with signals that are highly positively correlated within each clique that generate different beliefs across
cliques, even when there are opportunities to exchange information with individuals sharing less correlated signals. Thus, this model exemplifies how homophily and belief polarization can coexist in a rational environment.

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