Adversarial topology manipulation in power grids: A game-theoretic approach to critical infrastructure protection via network entropy

The resilience of critical infrastructure networks hinges on the coupling between topology and function, yet most robustness metrics ignore how intelligent adversaries exploit this interplay. We propose a bilevel game-theoretic framework that uses Network Topology Entropy (NTE), which is a data-free measure of structural uniformity, to identify critical links under strategic attacks. The attacker minimizes NTE by removing lines to fragment the network, while the defender mitigates impact via optimal power flow re-dispatch. Despite the nonconvex, logarithmic nature of NTE, we exactly reformulate the bilevel problem as a tractable Mixed-Integer Linear Program (MILP) using KKT-based linearization and a tailored piecewise-linear entropy approximation. Evaluated on IEEE 14- to 118-bus systems, our method shows that NTE strongly correlates with post-attack load loss and uncovers high-impact targets missed by centrality- or flow-based heuristics. Hardening the top-10 lines identified by our approach reduces load shedding by over 63% in the 39-bus system. This work establishes NTE as a data-light, interpretable metric for adversarial stress testing and offers a generalizable paradigm for probing structure–function resilience in cyber–physical networks.