This paper examines games on networks with linear best responses, which allow for the analysis of how interaction structures influence agents’ strategic behavior. Special attention is given to intervention issues in such models, particularly in selecting optimal intervention strategies aimed at maximizing the central planner’s objective function. Two main control policies are analyzed: individual agent incentives and modifications of the interaction structure. The concept of a representative agent is introduced to simplify equilibrium analysis and control problems in games on networks. Both aggregate outcome maximization problems and adversarial scenarios between competing central planners are considered. Analytical conditions are derived to determine whether controlling the interaction structure is more effective than influencing individual incentives. Numerical experiments confirm the theoretical results and demonstrate their applicability to different types of network structures.