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 discrete choice models. We show that the problem of finding an optimal interdiction strategy for the defender in the rational setting is NP-hard. The resulting optimization is in fact non-convex and additionally, involves complex terms that sum over exponentially many paths. We tackle these computational challenges by presenting new efficient approximation algorithms with bounded solution guarantees. First, we address the exponentially-many-path challenge by proposing a polynomial-time dynamic programming-based formulation. 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. Second, we identify a restricted problem that is convex and hence gradient-based methods find the global optimal solution for this restricted problem. We further identify mild conditions under which this restricted problem provides a bounded approximation for the original problem.

翻译：本文研究Stackelberg网络阻断博弈——一类重要的博弈问题：防御者首先将（随机化的）防御资源分配给图上的若干关键节点，而进攻者则据此选择其攻击路径。我们考虑有界理性的攻击者，其响应模型基于经典Logit型离散选择模型的动态形式。我们证明，在理性设定下求解防御者的最优阻断策略是NP-hard问题。该优化问题不仅非凸，且涉及对指数级路径求和的复杂项。为应对这些计算挑战，我们提出具有有界解保证的新型高效近似算法。首先，通过提出基于多项式时间动态规划的求解框架，解决指数级路径难题。进而证明非凸目标的梯度可在多项式时间内计算，从而可利用梯度法高效求解问题。其次，我们识别出一个具有凸性的受限问题，梯度法可为其找到全局最优解。进一步，我们在温和条件下证明该受限问题可为原问题提供有界近似解。