On a Network Centrality Maximization Game

Virtual Informal Systems Seminar (VISS)
Centre for Intelligent Machines (CIM) and Groupe d'Etudes et de Recherche en Analyse des Decisions (GERAD)

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Meeting ID: 845 1388 1004
Passcode: VISS

Speaker: Giacomo Como, Professor, Department of Mathematical Sciences, Politecnico di Torino

Abstract:
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.