Abstract
Game-theoretic security resource allocation problems have generated significant interest in the area of designing and developing security systems. These approaches traditionally utilize the Stackelberg game model for security resource scheduling in order to improve the protection of critical assets. The basic assumption in Stackelberg games is that a defender will act first, then an attacker will choose their best response after observing the defender’s strategy commitment (e.g., protecting a specific asset). Thus, it requires an attacker’s full or partial observation of a defender’s strategy. This assumption is unrealistic in real-time threat recognition and prevention. In this paper, we propose a new solution concept (i.e., a method to predict how a game will be played) for deriving the defender’s optimal strategy based on the principle of acceptable costs of minimax regret. Moreover, we demonstrate the advantages of this solution concept by analyzing its properties.
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Notes
- 1.
A defender’s knowledge of both players’ payoff matrices and an attacker’s knowledge of their own payoff matrix.
- 2.
While surveillance information can be represented by some imprecise probability theories [7], due to space restrictions, in this paper we focus on probability theory.
- 3.
Regret is an emotion associated with decisions which yield undesirable outcomes.
- 4.
Formally, in a two-player game, a probability distribution p for the pure strategies of a given player i (\(A_i=\{a_1,\dots ,a_n\}\)) is an equalizer if and only if there exists \(c\in \mathfrak {R}\) (\(\mathfrak {R}\) is the set of real numbers) and any pure strategy \(b_j\) for their opponent, s.t. the following equation holds \(\Sigma _{t=1}^{n} p(a_{t}) u_{i}(a_{t},b_{j})=c\).
- 5.
\(k=l\) means that both players select the same target (i.e., the attacker loses), while \(i\ne j\) and \(s\ne r\) mean that players select different targets (i.e., the attacker wins).
- 6.
Since a defender may have multiple available security resources, our Linear Programs will also consider this situation based on Definition 3.
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Ma, W., Liu, W., McAreavey, K. (2015). Game-Theoretic Resource Allocation with Real-Time Probabilistic Surveillance Information. In: Destercke, S., Denoeux, T. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2015. Lecture Notes in Computer Science(), vol 9161. Springer, Cham. https://doi.org/10.1007/978-3-319-20807-7_14
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