Enforcing social behavior in an Ising model with complex neighborhoods

We consider the problem of enforcing desired behavior in a population of individuals modeled by an Ising model. Although there is a large literature dealing with social interaction models, the problem of controlling behavior in a system modeled by the Ising model seems to be an unexplored field. First, we provide and analytically characterize an optimal policy that may be used to achieve this objective. Second, we show that complex neighborhoods highly influence the decision making process. Third, we use Lagrange multipliers associated to some constraints of a related problem to identify the role of individuals in the system.