  Network games study the strategic interaction of agents connected through a
network. Interventions in such a game -- actions a coordinator or planner may
take that change the utility of the agents and thus shift the equilibrium
action profile -- are introduced to improve the planner's objective. We study
the problem of intervention in network games where the network has a group
structure with local planners, each associated with a group. The agents play a
non-cooperative game while the planners may or may not have the same
optimization objective. We model this problem using a sequential move game
where planners make interventions followed by agents playing the intervened
game. We provide equilibrium analysis and algorithms that find the subgame
perfect equilibrium. We also propose a two-level efficiency definition to study
the efficiency loss of equilibrium actions in this type of game.
