Multistage Attack Graph Security Games: Heuristic Strategies, with Empirical Game-Theoretic Analysis

Figure 4

Level-0 value-propagation attack strategy. In this example, the discount factor is . The attacker rewards at goal nodes are . If the attacker performs exploits and to activate the -node , he has to pay a cost of and the corresponding activation probability is . In addition, if the attacker performs the exploit to activate the goal node , his cost is and the activation probability is . Algorithm 2 works as follows. Suppose that the propagation parameter , then Algorithm 2 estimates the propagated attack value from postconditions and to precondition as and . Similarly, Algorithm 2 estimates the propagated attack value from postconditions , , and to precondition as , , and . The attack values of other nodes of which postconditions are the goal nodes are estimated similarly. The attack value of node will be computed based on the attack value of its postconditions , , , and so on. This process will continue until all inactive nodes are examined.