The Key Class in Networks

This paper examines optimal targeting of multiple network players from a new perspective, focusing on classes of players holding similar network positions – and thus fulfilling similar network roles – as captured by the graph theoretic notion of equitable partition. Unlike existing centrality measures, we show that analysing the network game with local payoff complementarities under symmetry brings out new insights about the relative influence of classes of similarly positioned network players on the Nash equilibrium activity. Our analysis introduces two novel class-based centrality measures with broad theoretical and empirical applicability that geometrically characterise the key class whose removal results in the maximal reduction of aggregate and per-capita network activity, respectively.