2022/11/07 by Costanza Catalano, Catalano, Costanza, Maria Castaldo +5 · 2 citations
Decision Sciences · Economics, Econometrics and Finance · Physics and Astronomy · #91A43 #91D30 #Computer Science and Game Theory (cs.GT) #Economic theories and models #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Game Theory and Applications #Opinion Dynamics and Social Influence #Probability (math.PR) #Social and Information Networks (cs.SI) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2211.03685
openalex publication_date 2022/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 di 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 di 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.