The Adversarial Risk Analysis Approach - 1709 Words

Source: Figure 3 (Rios and Insua, 2012) Source: Figure 4 (Rios and Insua, 2012) Source: Figure 5 (Rios and Insua, 2012) Source: Figure 6 (Rios and Insua, 2012) The Adversarial Risk Analysis Approach relaxes the common knowledge assumption in order to make this model more realistic. If the Defender’s decision problem is a standard decision analysis problem, shown in Figure 3, with the Attacker’s decision node regarded as a random variable. Then her decision tree in Figure 4 illustrates the uncertainty about the Attacker’s decision by replacing A (in a square, Fig 3) with A (in a circle, Fig 3). (Rios and Insua 2012) Once the Defender has already assessed pD(S | d, a, v) and uD(d, s, v), she needs pD(A | d), which is†¦show more content†¦The Defender’s decision is illustrated as a random variable as it is not under control in the Attacker’s analysis. The arrow from D (in a circle, Fig 5) to A (in a square, Fig 5) in the influence diagram demonstrates that he will know the Defender’s decision while he has to decide. The Defender’s private information v, is not known by the Attacker, therefore his uncertainty is demonstrated through a probability distribution pA(V), illustrating the Attacker’s previous beliefs about the Defender’s private information. Assuming the Defender analyses the Attacker’s decision, knowing that he is an expected utility maximiser and uses Bayes’s rule to discover about the Defender’s private information from monitoring of her defence decision. Consequently, the arrow in the influence diagram from V (in a circle, Fig 5) to D (in a circle, Fig 5), represents probabilistic dependence, is to be inverted to acquire the Attacker’s subsequent beliefs about v: pA(V|D=d), yet to acquire this it is needed to assess pA(D|v). (Rios and Insua 2012) If the Defender knew the Attacker’s utility function uA(a,s,v) and the probabilities pA(S|d,a,v) and pA(V|d), she could predict his decision a*(d) for any d ∈ D by solving backwards the tree in Figure 6, followed by computing his expected utility ψA. - Compute at chance node S: ψA(d,a,v) for each (d,a,v) as in Equation (2). - Compute for