title: Competition among networks highlights the power of the weak.
abstract: The unpreventable connections between real networked systems have recently called for an examination of percolation, diffusion or synchronization phenomena in multilayer networks. Here we use network science and game theory to explore interactions in networks-of-networks and model these as a game for gaining importance. We propose a viewpoint where networks choose the connection strategies, in contrast with classical approaches where nodes are the active players. Specifically, we investigate how creating paths between networks leads to different Nash equilibria that determine their structural and dynamical properties. In a wide variety of cases, selecting adequate connections leads to a cooperative solution that allows weak networks to overcome the strongest opponent. Counterintuitively, each weak network can induce a global transition to such cooperative configuration regardless of the actions of the strongest network. This power of the weak reveals a critical dominance of the underdogs in the fate of networks-of-networks.
authors.affiliation: National Center for Biotechnology Information, National Library of Medicine, National Institutes of Health, Bethesda, Maryland 20894, USA.
authors.forename: Jaime
authors.initials: J
authors.lastname: Iranzo
authors.affiliation: Laboratory of Biological Networks, Center for Biomedical Technology (UPM), Pozuelo de Alarcón, 28223 Madrid, Spain.|Complex Systems Group, Universidad Rey Juan Carlos, Móstoles, 28933 Madrid, Spain.|Grupo Interdisciplinar de Sistemas Complejos (GISC), Madrid, Spain.
authors.forename: Javier M
authors.initials: JM
authors.lastname: Buldú
authors.affiliation: Grupo Interdisciplinar de Sistemas Complejos (GISC), Madrid, Spain.|Centro Nacional de Biotecnología, CSIC. c/Darwin 3, 28049 Madrid, Spain.
authors.forename: Jacobo
authors.initials: J
authors.lastname: Aguirre
mesh_terms: D000465:Algorithms; D003195:Computer Communication Networks; D005716:Game Theory; D006801:Humans; D008962:Models, Theoretical; D016571:Neural Networks, Computer