Who's Who in Networks. Wanted: the Key Player

Authors: Coralio Ballester, Antoni Calvó-Armengol and Yves Zenou

Econometrica, Vol. 74, No 5, 1403--1417, January, 2006

Finite population noncooperative games with linear-quadratic utilities, where each player decides how much action she exerts, can be interpreted as a network game with local payoff complementarities, together with a globally uniform payoff substitutability component and an own-concavity effect. For these games, the Nash equilibrium action of each player is proportional to her Bonacich centrality in the network of local complementarities, thus establishing a bridge with the sociology literature on social networks. This Bonacich-Nash linkage implies that aggregate equilibrium increases with network size and density. We then analyze a policy that consists of targeting the key player, that is, the player who, once removed, leads to the optimal change in aggregate activity. We provide a geometric characterization of the key player identified with an intercentrallty measure, which takes into account both a player's centrality and her contribution to the centrality of the others.

This paper originally appeared as Barcelona GSE Working Paper 178