Optimal Targets in Small and Large Networks, Using Game Theory

We define a model of peer effects where the intra-group externality is rooted on the network of bilateral influences in the population, rather than consisting on an average effect. Using game theory, we then map the geometric intricacies of this network structure to the distribution of equilibrium outcomes. Nash equilibrium turns out to be well-described by Bonacich network centrality, used in sociology. We then exploit the network variance of peer effects to identify optimal network targets, key groups. Key groups correspond to the highest inter-central groups, a new network measure that subsumes collective optimality concerns. Although intended for small networks, the key group policy coupled with a more standard geometric attack turns out to be optimal for large scale free networks when 2.33 < fl < 3. We then apply our model to terrorist networks, and identify the Achilles heel of the 11S cell.