  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.

Optimization and Control