Privacy-constrained network formation

We study the effects of privacy concerns on social network formation. Each individual decides which others to form links with. Links bring direct benefits from friendship but also lead to the sharing of information via a percolation process. Privacy concerns are modeled as a disutility that the individual suffers as a result of her private information being acquired by others. We specify conditions under which pure-strategy equilibria exist and characterize both pure-strategy and mixed-strategy equilibria. The resulting equilibrium networks feature clustered connections and homophily. Clustering emerges because if player a is friend with b and b is friend with c, then a's information is likely to be shared indirectly with c anyway, making it less costly for a to befriend c. Homophily emerges because small additional benefits of friendship within a group make linkages and thus information sharing within that group more likely, further increasing the likelihood within-group links.