Shadow links

We propose a framework of network formation where players can form two types of links: public links are observed by everyone and shadow links are only observed by neighbors. We introduce a novel solution concept called rationalizable peer-confirming pairwise stability, which generalizes Jackson and Wolinsky (1996)'s pairwise stability notion to accommodate shadow links. We then study the case when public links and shadow links are perfect substitutes and relate our concept to pairwise stability. Finally, we consider two specific models and show how false beliefs about others' behavior may lead to segregation in friendship networks with homophily, reducing social welfare.