Defending a capacitated series-parallel system with imperfect fault coverage

Resource allocation in attack-defense games strongly shapes system reliability. Prior work often treats failures as isolated single-node events, overlooking imperfect fault coverage: an attacked component can trigger cascading failures and disable an entire subsystem. We model imperfect coverage with the Universal Generating Function (UGF) to compute survival probability, and embed it in a sequential game. The defender commits resources first; the attacker observes this choice and allocates resources to minimize reliability. Using backward induction, we derive the defender's optimal strategy from the attacker's best response. Numerical experiments demonstrate the model's applicability. Results show that imperfect coverage can substantially affect reliability and may cause both gradual and abrupt shifts in attacker-defender strategies. Sensitivity analyses assess how competition intensity and resource budgets influence these outcomes.