Introduction

Introduction:
We are recommending use of a sequential Defend- Attack model to structure the problem. 1 2 Here, Adversarial Risk Analysis (ARA) aims to support one of the participants the defender (here, Airport authority as She), who uses decision analytic approach to solve her decision making problem. Defender can utilize ARA to find the optimal allocation of available security resources to protect a single component of the airport system. Here, defender is government or private security body, who is protecting airport from the terrorist organization (here, taken as He), the Attacker. According to researchers, the defender’s problem is multi-objective in nature so as the Attacker’s. Therefore, support provided by ARA is customary to only one opponent, which is Defender.
The Model:
By using a sequential Defend- Attack model an influence diagram has been generated by the researchers. 4 The influence diagram depicts that, to protect the terminal building the airport authorities deploy the preventive measures. The Attacker will observe the deployment and will decide whether to launch an attack or not. From the Attacker’s side depending upon the number of terrorists after observing the activities of airport authorities, he might thing of changing the severity of the attack. In the situation of the successful attack launch by the Attacker, the Defender will try to recover from it and minimize the after effects of the attack by calling in Special Police Force (SPF).
The influence diagram is bi-agent; the nodes on the left side belong to defender and the nodes on the right side belong to Attacker. A node corresponds to the Defender’s portfolio of preventive measures is ‘Prev. measures’, denoted by x and a set of portfolios will be designated D1. The deployment of recovery measures is denoted by the node called ‘Counter measures’. There is no result associated with that because it is an automatic response under the circumstances of successful attack. If attack is failed there will be no additional resources will be deployed. After observing Defender’s moves the Attacker takes a decision, which is denoted by a node called ‘Attacker Decision’. The set of all possible attacks a will be denoted by A.
Figure1. Influence diagram 4
The relevant uncertainties for this problem are: (1) the preliminary result of the attack, s1, represented by the node “Result”, which depends probabilistically on (x, a) ? D1 × A, and will be described by the random variable S1 taking values in the set S1; and (2) its final outcome after the intervention of the SPF, s2, represented by the node “Final Result”, which will be described by the random variable S2 taking values in S2. Concerning the multiple attributes of the problem, detailed later on, we assume that the consequences for the Defender, represented by the chance node “Cons. airport”, will depend on (x, s1, s2), i.e., the effort spent in implementing protective measures, the initial impact of the attack and its final result after the eventual intervention of the SPF. Then, she will get her utility uD. Similarly, the multiple consequences for the Attacker, summarized at the chance node “Cons. attacker”, will depend on (a, s1, s2), i.e., the effort spent in launching the attack, and the related initial and final outcomes. He will then get his utility uA.
The elements in the sets D1, A, S1 and S2 are as follow.
• D1: We consider all feasible portfolios x = (x1, x2, x3, x4, x5) of measures respectively, represent the number of additional cameras, metal detector units, X-ray devices, police and private security members deployed. They have corresponding unit costs c j, j = 1 . . . , 5 over the incumbent planning period. Then, if we denote by B the available budget, the feasible portfolios of preventive measures should satisfy,
c1x1 + c2x2 + c3x3 + c4x4 + c5x5 ? B,
x1, x2, x3, x4, x5 ? 0,
x1, x2, x3, x4, and x5 are integers.
• A: here, model the Attacker as an organized group composed of between one and five terrorists. Therefore, we shall consider the number of terrorists actually performing the attack against the terminal building as the decision variable for the Attacker, i.e. a ? A = {0, 1, 2, 3, 4, 5}. This includes the possibility of no attack through the choice a = 0.
• S1: The possible values for s1 are 0, 1 . . . . , a, representing how many terrorists managed to get into the terminal building. The rest would have been killed or detained during the attack, or might have avoided being captured, as later explained. If s1 = 0, the attack fails and the problem is over. Irrespective of the result of the attack, some casualties could also occur among the defenders. We will discuss this issue later on, when analyzing the Defender’s problem.
• S2: We assume that the terminal building will be always recovered by the SPF. This has been the case in similar recent episodes: security forces took hold back of the situation sooner or later. However, we are interested in how many terrorists will be killed or detained.
• The possible values in S2 as s2 ? {0, 1 . . . , s1}, representing the number of terrorists killed. The remaining terrorists, s1 ? s2, will be detained. At this stage, we explicitly rule out the possibility of some terrorists getting away from the terminal building. Besides, additional casualties could also occur among the defenders.
The Defender’s Problem:

The Defender’s dynamics:
Figure2. Influence diagram for Defender’s problem 5
1. She invests (x1, x2, x3, x4, x5), incurring in a cost c1x1+c2x2+c3x3+c4x4+c5x5. Here, (x1, x2, x3) serve to reduce the likelihood of any prohibited item being introduced in the airside or in security restricted areas, as well as increase the probability of detecting suspect people trying to enter into the ATC Tower with criminal intentions and (x4, x5) serve to deter the actions of potential attackers.
2. If attack is successful, she calls on the SPF, so as to get back the control over the terminal building.
3. She faces the multiple consequences cD in relation with the eventual terrorist attack against the terminal building, and the recovery from it after the intervention of the SPF.
4. She attains her (multi objective) utility.
The consequences for the Defender:
1. Lives and injuries: When the first strike of terrorists takes place, everybody present in the terminal building could be in injury or life danger, even with a possibility of being taken as hostage by the terrorists. This affects passengers and staff inside or near the facilities in the terminal building. Additional casualties among SPF members, security personnel or civilians could also happen during recovery actions. We take all this into account defining a random variable y ? {0, 1 . . . , m}, representing the number of casualties or severely injured people on the Defender’s side, where m stands for the maximum theoretical number of victims. We assume a fixed cost of life clife on the Defender’s side, irrespective of their affiliation. For simplicity, we assume the same consequences for a killed or badly injured person. 6 7
2. Flight diversion and cancellation: Here, we can aggregate all the events such as, flight diversion or cancelation into a single quantity f. It seems reasonable to assume that the consequences (in terms of costs) for airport authorities will be similar, regardless of the number of terrorists actually succeeding in accessing the terminal building, except for the case in which only one attacker succeeds (s1 = 1), for which we will assume a lesser impact. We shall also take into account the inherent uncertainty on the value of f, expressed through a probability distribution pD (f|s1). 8
3. Image consequences: When a security incident occurs, this will typically yield an immediate deterioration on the image of the airport as perceived by customers, even if no life or injury damage occurs. This “panic effect” is a main objective for the Attacker. We shall subsume: (1) Airport security; (2) Aircraft security and safety; and (3) National security these effects into a single variable, g, and use a probability distribution pD (g|a) to express the Defender’s uncertainty about it, whose expected value will increase with the number a of terrorists.