# On a Centrality Maximization Game

arXiv: https://arxiv.org/abs/1911.06737 · HTML: https://mlsanity.com/paper/1911.06737/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Nov 2019.

## Built on by (most cited first, 1 of 1)

- [Wisdom of Crowds Through Myopic Self-Confidence Adaptation](https://mlsanity.com/paper/2506.18195/) (2025)

## Abstract (arXiv)

The Bonacich centrality is a well-known measure of the relative importance of nodes in a network. This notion is, for example, at the core of Google's PageRank algorithm. In this paper we study a network formation game where each player corresponds to a node in the network to be formed and can decide how to rewire his m out-links aiming at maximizing his own Bonacich centrality, which is his utility function. We study the Nash equilibria (NE) and the best response dynamics of this game and we provide a complete classification of the set of NE when m=1 and a fairly complete classification of the NE when m=2. Our analysis shows that the centrality maximization performed by each node tends to create undirected and disconnected or loosely connected networks, namely 2-cliques for m=1 and rings or a special "Butterfly"-shaped graph when m=2. Our results build on locality property of the best response function in such game that we formalize and prove in the paper.