Optimal defense with variable number of overarching and individual protections

The article considers a system consisting of identical elements. Each element can be protected individually. The groups of elements can have overarching protection. To destroy an element having both types of protections the attacker must always penetrate/destroy the overarching protection and then destroy the individual protection of the element. Both the attacker and the defender have limited resources. The resources needed to defend and attack the overarching protection are fixed, as is also the number of elements that can be protected by single overarching protection. The defender chooses the number of overarching protections and the number of individual protections within each protected group to minimize the expected damage caused by the attack. The attacker chooses the number of attacked overarching protections and after attacking the overarching protections it chooses the number of attacked elements to maximize the expected damage. The three period minmax game is formulated and an enumerative procedure for its solving is suggested. The influence of the game parameters on the optimal defense and attack strategies is discussed.