Tackling Stackelberg Network Interdiction against a Boundedly Rational Adversary

TL;DR

This paper develops efficient approximation algorithms for Stackelberg network interdiction games with a boundedly rational adversary, addressing computational challenges in finding optimal defense strategies against complex, logit-based adversary responses.

Contribution

It introduces polynomial-time algorithms for approximating solutions in complex interdiction games with bounded rationality, including a dynamic programming formulation and a convex restricted problem.

Findings

Polynomial-time dynamic programming formulation for exponential path sums

Gradient-based methods efficiently solve the non-convex interdiction problem

A convex restricted problem provides bounded approximation guarantees

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 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.