Sudipta Sarangi - Virginia Tech

Network Formation with Multigraphs and Strategic Comlementarities.

Abstract:  This paper examines the formation of one network G when connections in a second network H are inherited under two scenarios: (i) H is asymmetric allowing for a wide range of networks called nested split graphs, and (ii) H is symmetric in Bonacich centrality. The bulk of our paper assumes that both G and H are interdependent because the respective actions in each are (weak) strategic complements.This complementarity creates a “"silver spoon”" effect whereby those who inherit high Bonacich centrality in H will continue to have high Bonacich centrality in G. There is however a "“silver lining"”: depending on the costs of link formation, the formed network G may allow for an improvement in centrality. As an application, we introduce an overlapping generations models to analyze intergenerational transmission of
inequality through networks. Finally, we explore the implications of actions being strategic substitutes across networks. This can lead to a “"leisure class”" à la Veblen where well connected agents in H establish no links in G, and those with no connections in H form all the links in G. Our analysis provides insight into preferential attachment, how asymmetries in one network may be magni…ed or diminished in another, and why players with links in one network may form no links in another network.