A Model of the Formation of Multilayer Networks

We study the formation of multilayer networks where payoffs are determined by the degrees in each network and explore distinct network relationships by allowing for inter-network and intra-network spillovers through five properties: supermodularity and submodularity for internetwork spillovers, and convexity, concavity, and strategic complementarity for intra-network spillovers. We show the existence of multilayer equilibrium networks, provide a characterization and examine how inter-network spillovers determine the pattern of links between players.