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We study a network formation game where n players, identified with the nodes of a directed graph to be formed, choose where to wire their outgoing links in order to maximize their PageRank centrality. Specifically, the action of every player i consists in the wiring of a predetermined number d(i) of directed out-links, and her utility is her own PageRank centrality in the network resulting from the actions of all players. We show that this is a potential game and that the best response correspondence always exhibits a local structure in that it is never convenient for a node i to link to other nodes that are at incoming distance more than d(i) from her. We then study the equilibria of this game determining necessary conditions for a graph to be a (strict, recurrent) Nash equilibrium. Moreover, in the homogeneous case, where players all have the same number d of out-links, we characterize the structure of the potential maximizing equilibria and, in the special cases d=1 and d=2, we provide a complete classification of the set of (strict, recurrent) Nash equilibria. Our analysis shows in particular that the considered formation mechanism leads to the emergence of undirected and disconnected or loosely connected networks. This is a joint work with Costanza Catalano, Maria Castaldo, and Fabio Fagnani.

Biography: Giacomo Como is a Professor at the Department of Mathematical Sciences, Politecnico di Torino, Italy. He is also a Senior Lecturer at the Automatic Control Department, Lund University, Sweden. He received the B.Sc., M.S., and Ph.D. degrees in Applied Mathematics from Politecnico di Torino, in 2002, 2004, and 2008, respectively. He was a Visiting Assistant in Research at Yale University in 2006--2007 and a Postdoctoral Associate at the Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, from 2008 to 2011. He is recipient of the 2015 George S. Axelby Outstanding Paper Award. His research interests are in dynamics, information, and control in network systems with applications to cyber-physical systems, infrastructure networks, and social and economic networks.