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Multi-Agent Decentralized Network Interdiction Games

In this work, we introduce decentralized network interdiction games, which model the interactions among multiple interdictors with differing objectives operating on a common network. As a starting point, we focus on decentralized shortest path interdiction (DSPI) games, where multiple interdictors try to increase the shortest path lengths of their own adversaries, who all attempt to traverse a common network. We first establish results regarding the existence of equilibria for DSPI games under both discrete and continuous interdiction strategies. To compute such an equilibrium, we present a reformulation of the DSPI games, which leads to a generalized Nash equilibrium problem (GNEP) with non-shared constraints. While such a problem is computationally challenging in general, we show that under continuous interdiction actions, a DSPI game can be formulated as a linear complementarity problem and solved by Lemke's algorithm. In addition, we present decentralized heuristic algorithms based on best response dynamics for games under both continuous and discrete interdiction strategies. Finally, we establish theoretical bounds on the worst-case efficiency loss of equilibria in DSPI games, with such loss caused by the lack of coordination among noncooperative interdictors, and use the decentralized algorithms to empirically study the average-case efficiency loss.