On a Network Centrality Maximization Game

Costanza Catalano (), Maria Castaldo (), Giacomo Como () and Fabio Fagnani ()
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Costanza Catalano: Department of Economics, Statistics and Research, Bank of Italy, 00044 Frascati, Italy
Maria Castaldo: GIPSA-lab, Université de Grenoble Alpes, Centre national de la recherche scientifique, INRIA, Grenoble INP, F-38000 Grenoble, France
Giacomo Como: G. L. Lagrange Department of Mathematical Sciences, Polytechnic University of Turin, 10129 Turin, Italy; and Department of Automatic Control, Lund University, 22100 Lund, Sweden
Fabio Fagnani: G. L. Lagrange Department of Mathematical Sciences, Polytechnic University of Turin, 10129 Turin, Italy

Mathematics of Operations Research, 2025, vol. 50, issue 3, 2112-2140

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.

Keywords: Primary: 91A43; secondary: 91D30; network formation games; network centrality; ordinal potential games (search for similar items in EconPapers)
Date: 2025
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