Facility location and restoration games

Effective recovery of interdependent infrastructure systems after natural disasters requires coordination between multiple infrastructure owners, such as power and telecommunications utilities. If infrastructure owners make restoration decisions in isolation from one another, then recovery maybe piecemeal. A fundamental understanding of these interdependencies can provide insights to incentivize shared restoration that benefit all infrastructure users, with the goal to maximize the social welfare even in a non-cooperative setting. We introduce a non-cooperative facility location and restoration game on a layered network, where each layer belongs to a player, to model the recovery of interdependent infrastructure systems after disasters. The goal of the model is to plan short term post-disaster recovery. The players want to minimize the cost to satisfy their own demand by restoring network components, and each player can serve the other players' demands if they are paid a fee to do so. We propose exact and approximate algorithms to set incentives (fees) so that the players' actions at equilibrium are aligned with a social optimum of the system, which minimizes the total cost. We present a case study in which we consider the recovery efforts of telecommunication infrastructure companies and provide results for the facility location and restoration games. The models and proposed algorithms can be used to set policy, inform the structure of inter-agency mutual aid partnerships to support disaster recovery, and negotiate inter-agency usage fees prior to a disaster to ease shared recovery efforts.