Who's who in networks. Wanted: the key group

Abstract

Ballester, Calv ́o-Armengol, and Zenou (2006, Econometrica, 74/5, pp. 1403-17) show that in a network game with local payoff complementarities, together with global uniform payoff substitutability and own concavity effects, the intercentrality measure identifies the key player - a player who, once removed, leads to the optimal change in overall activity. In this paper we search for the key group in such network games, whose members are, in general, different from the players with the highest individual intercentralities. Thus the quest for a single target is generalized to a group selection problem targeting an arbitrary number of players, where the key group is identified by a group intercentrality measure. We show that the members of a key group are rather nonredundant actors, i.e., they are largely heterogenous in their patterns of ties to the third parties.