Being Central on the Cheap: Stability in Heterogeneous Multiagent Centrality Games

TL;DR

This paper explores how agents form stable networks based on various centrality measures, revealing diverse stable structures and conditions under which networks remain stable despite costs.

Contribution

It introduces an axiomatic framework for predicting stable networks with heterogeneous centrality preferences, extending classical models to include a broader set of centrality measures.

Findings

Stable networks exhibit core-periphery and rich club features.

A simple variation makes the model universal, allowing any network to be stable.

Structural properties of networks can reveal information about agent utilities.

Abstract

We study strategic network formation games in which agents attempt to form (costly) links in order to maximize their network centrality. Our model derives from Jackson and Wolinsky's symmetric connection model, but allows for heterogeneity in agent utilities by replacing decay centrality (implicit in the Jackson-Wolinsky model) by a variety of classical centrality and game-theoretic measures of centrality. We are primarily interested in characterizing the asymptotically pairwise stable networks, i.e. those networks that are pairwise stable for all sufficiently small, positive edge costs. We uncover a rich typology of stability: - we give an axiomatic approach to network centrality that allows us to predict the stable network for a rich set of combination of centrality utility functions, yielding stable networks with features reminiscent of structural properties such as "core periphery" and "rich club" networks. - We show that a simple variation on the model renders it universal, i.e. every network may be a stable network. - We also show that often we can infer a significant amount about agent utilities from the structure of stable networks.