On a Network Centrality Maximization Game

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-16 DOI:10.1287/moor.2022.0251

Costanza Catalano, Maria Castaldo, Giacomo Como, Fabio Fagnani

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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 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.Funding: This research was carried out within the framework of the Ministero dell’Università e della Ricerca (MIUR)-funded Progetto di Eccellenza of the Dipartimento di Scienze Matematiche G. L. Lagrange, Politecnico di Torino [CUP: E11G18000350001]. It received partial support from the MIUR-funded project PRIN 2017 “Advanced Network Control of Future Smart Grids” and from the Compagnia di San Paolo.

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论网络中心性最大化博弈

我们研究的是一个网络形成博弈，在这个博弈中，n 个参与者（与待形成的有向图的节点相对应）选择在哪里连接他们的外向链接，以最大化他们的 PageRank 中心度。具体来说，每个玩家 i 的行动都包括预先确定数量 di 的有向外链的布线，而她的效用就是她自己在所有玩家行动所形成的网络中的 PageRank 中心度。我们证明这是一个潜在博弈，而且最佳响应对应关系总是呈现局部结构，即节点 i 绝不方便链接到与她的传入距离大于 di 的其他节点。然后，我们研究了这个博弈的均衡，确定了一个图成为（严格的、经常性的）纳什均衡的必要条件。此外，在同质情况下，即所有博弈者都有相同数量的外链 d，我们描述了潜在最大化均衡的结构，而在 d = 1 和 d = 2 的特殊情况下，我们提供了（严格、循环）纳什均衡集的完整分类。我们的分析特别表明，所考虑的形成机制会导致出现无向、断开或松散连接的网络：本研究是在都灵理工大学 G. L. Lagrange 数学科学系都灵大学和研究部（MIUR）资助的杰出项目[CUP: E11G18000350001]框架内进行的。它得到了 MIUR 资助的 PRIN 2017 项目 "未来智能电网的高级网络控制 "和 Compagnia di San Paolo 的部分支持。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.