Being Central on the Cheap: Stability in Heterogeneous Multiagent Centrality Games
This work provides a foundational understanding of network stability for researchers studying strategic network formation and agent behavior, offering insights into how different centrality measures and agent heterogeneity influence network structure.
This paper investigates strategic network formation where agents create costly links to maximize their network centrality, extending the Jackson-Wolinsky model to include heterogeneous agent utilities and various centrality measures. The research characterizes asymptotically pairwise stable networks, revealing a rich typology of stability, including core-periphery and rich club structures, and demonstrates that a simple model variation can make any network stable.
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.