Key Group in Networks and its Optimal Size: Accounting for Individual Ex Ante Heterogeneity

Abstract

We consider a network game studied in Ballester, Calvo-Armengol, and Zenou (2006, Econometrica, 74/5, pp. 1403-17), where an intercentrality measure identifies the key player - a player who, once removed, leads to the optimal change in overall activity. This paper in searching for the key group takes into account players' ex ante exogenous heterogeneity, and shows that the outcome can dramatically change once these observable differences are accounted for. Further, introducing costs of targeting players, we endogenize the size of the key group. Weighted and nonweighted group intercentrality measures that depend only on the initial network configuration help to identify the key player/group.