Tackling Stackelberg Network Interdiction against a Boundedly Rational Adversary
IJCAI 2024(2024)
Abstract
This work studies Stackelberg network interdiction games — an important class of games in which a defender first allocates (randomized) defense resources to a set of critical nodes on a graph while an adversary chooses its path to attack these nodes accordingly. We consider a boundedly rational adversary in which the adversary’s response model is based on a dynamic form of classic logit-based (quantal response) discrete choice models. The resulting optimization is non-convex and additionally, involves complex terms that sum over exponentially many paths. We tackle these computational challenges by presenting new efficient algorithms with solution guarantees. First, we present a near optimal solution method based on path sampling, piece-wise linear approximation and mixed-integer linear programming (MILP) reformulation. Second, we explore a dynamic programming based method, addressing the exponentially-many-path challenge. We then show that the gradient of the non-convex objective can also be computed in polynomial time, which allows us to use a gradient-based method to solve the problem efficiently. Experiments based on instances of different sizes demonstrate the efficiency of our approach in achieving near-optimal solutions.
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Key words
Game Theory and Economic Paradigms -> GTEP: Noncooperative games,Constraint Satisfaction and Optimization -> CSO: Mixed discrete and continuous optimization
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