Ballester, C., A. Calvó-Armengol, and Y. Zenou
Econometrica – 75.4 (2006): 1403-1418. (Reviewed in NAJ Economics, 8)

Keywords: networks,key player,complementarities,linear-quadratic,Nash equilibrium,bonacich,katz,centrality

Abstract: 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 intercentrality measure, which takes into account both a player’s centrality and her contribution to the centrality of the others.