Intelligence and impact contests in systems with redundancy, false targets, and partial protection

The paper considers a system consisting of identical elements that can be intentionally attacked. The cumulative performance of the system elements should meet a demand. To prevent loss of demand the defender provides system redundancy (deploying genuine system elements (GEs) with cumulative performance exceeding the demand); deploys false elements (FEs), and protects the GEs. If the attacker cannot distinguish GEs and FEs, he chooses the number of elements to attack and attacks at random these elements distributing his resource evenly among the attacked elements. In order to get the information about the system the attacker allocates a part of his resource into the intelligence activity. Analogously, the defender allocates a part of his resource into the counter-intelligence activity. The attacker's strategy presumes distribution of his resource among the intelligence and attack effort and choice of the number of attacked elements. If the attacker wins the intelligence contest, he can identify both FEs and unprotected GEs ignoring the former ones and destroying the latter ones with negligible effort. The defender's strategy presumes distribution of his resource among the counter-intelligence and the three defensive actions. The paper considers a three-period non-cooperative minmax game between the defender and the attacker and presents an algorithm for determining the agents' optimal strategies.