Game Theory for Managing Security in Chemical Industrial Areas by Laobing Zhang & Genserik Reniers

Author:Laobing Zhang & Genserik Reniers
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

4.2 Interval CPP Game Definition

Recalling the payoff Formula (3.​8) (see Sect. 3.​2.​3) and the intrusion probability calculation Formula (3.​1) (see Sect. 3.​1), the attacker’s payoff can be re-written as Formula (4.1).

(4.1)

For each attacker parameter (i.e., the ), for the sake of convenience, denoting it as σ, assume that the defender does not know the exact value of σ and she knows that σ ∈ [σ min, σ max]. Since , we can easily derive that:

(4.2)

(4.3)

In this research, the defender is assumed to know the exact numbers of her own parameters. Therefore, in the Interval CPP game, the defender’s payoff matrix is the same as in the CPP game, while the attacker’s payoff matrix consists of an upper bound matrix and a lower bound matrix, as defined in Formulas (4.2) and (4.3). We denote the Interval CPP game as .

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