Econometrica: Sep, 2006, Volume 74, Issue 5
Who's Who in Networks. Wanted: The Key Player
Coralio Ballester, Antoni Calvó‐Armengol, Yves Zenou
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 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 , 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 , which takes into account both a player's centrality and her contribution to the centrality of the others.