How to Determine Key Players when Spillovers are Large

This paper examines the behavior of Katz–Bonacich centrality and key-player intercentrality in linear–quadratic network games when spillovers are large. This question is both important and empirically relevant, as it greatly simplifies the empirical testing of peer-effect models. We show that Katz–Bonacich centrality converges (up to scale) to the Perron eigenvector, while intercentrality diverges and loses all discriminatory power across nodes. Consequently, designing key-player policies becomes problematic: key-player rankings collapse, and no agent is more important than another when spillovers are sufficiently large.