Preventive strike vs. counter intelligence and protection for a target under attack

A defender protects a target from being attacked. It can carry out two kinds of strategies. One is passive defense strategy. The other is active defense strategy. When the defender executes the passive defense strategy, it can deploy camouflage to misinform the attacker. When the defender runs the active defense strategy, it strikes the attacker preventively. Then, the defender will reveals itself and therefore, the attacker detects the target without the intelligence contest. Depending on the strategy chosen by the defender, the attacker should succeed in double contest games to destroy the target. In the case of passive defense it should win the target intelligence and impact contests. In the case of active defense it should win the preventive strike and impact contests. The attacker allocates its resources among the intelligence, the impact and self-protection efforts, whereas the defender distributes its resources among the counter intelligence, protection and the preventive strike efforts. The attacker attempts to maximize the target vulnerability, but oppositely the defender desires to minimize it. The paper develops two non-cooperative two-period minmax games.