Strategic Network Inspection with Location-Specific Detection Capabilities
arxiv(2024)
摘要
We consider a two-person network inspection game, in which a defender
positions a limited number of detectors to detect multiple attacks caused by an
attacker. We assume that detection is imperfect, and each detector location is
associated with a probability of detecting attacks within its set of monitored
network components. The objective of the defender (resp. attacker) is to
minimize (resp. maximize) the expected number of undetected attacks. To compute
Nash Equilibria (NE) for this large-scale zero-sum game, we formulate a linear
program with a small number of constraints, which we solve via column
generation. We provide an exact mixed-integer program for the pricing problem,
which entails computing a defender's pure best response, and leverage its
supermodular structure to derive two efficient approaches to obtain approximate
NE with theoretical guarantees: A column generation and a multiplicative
weights update (MWU) algorithm with approximate best responses. To address the
computational challenges posed by combinatorial attacker strategies, each
iteration of our MWU algorithm requires computing a projection under the
unnormalized relative entropy. We provide a closed-form solution and a
linear-time algorithm for the projection problem. Our computational results in
real-world gas distribution networks illustrate the performance and scalability
of our solution approaches.
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