The Limit of Targeting in Networks

Network-based targeting is valuable in many applications such as diffusion of new technology, product promotion in marketing, among others. Nevertheless, how to quantitatively measure the effectiveness of targeting strategies remains a challenge. This paper studies a class of network games with strategic complements, where a designer can choose finite sequences of targeting interventions to maximize the aggregate action.

We propose an effectiveness index, called \emph{relative network synergy equivalent} (RNSE), to measure the effect of such network-based targeting interventions. The main results show that, regardless of the targeting policies, the network structures, a simple and unified upper bound for this index is $\sqrt{2}\approx 1.414$. Moreover, this upper bound is tight. For specific network structures such as the complete network and the bipartite network, we obtain explicit formulas and sharper bounds for the index. We also provide comparative analysis of this index across different targeting policies and across different underlying network structures.