Cost intervention in delinquent networks

This study investigates a novel intervention approach to network games, in which players are delinquents whose payoffs depend on the actions of their network neighbors. The social planner aims to manipulate the delinquency costs of players, seeking to minimize the total delinquency level. We consider two intervention scenarios. First, we consider binary interventions, where the planner can either increase the cost of an offender by a fixed amount; or leave its cost unchanged. The optimal intervention problem involves maximizing a submodular function. We establish a connection between cost and structural intervention in networks. Next, we consider continuous levels of intervention, where the planner can choose how much to increase the cost of an offender. We show that the optimal intervention problem is a tractable convex optimization if the intervention function is concave. We provide a characterization of the optimal intervention which is highly related to players’ centralities in the network. We further discuss the interior solution and apply our result to nested split graphs.