具有可加效用的证券对策鞍点均衡的刻画
On the Characterization of Saddle Point Equilibrium for Security Games with Additive Utility
摘要：
在这项工作中，我们调查了攻击者和防御者之间的安全博弈，最初提出的\cite{emadi2019security}。众所周知，证券博弈的组合性质导致了一个大的成本矩阵。因此，计算玩家的价值和最优策略在计算上变得昂贵。在这项工作中，我们分析了一类特殊的零和游戏，其中的支付矩阵具有特殊的结构，这是由于{ \it添加剂性质}的效用函数。基于变分原理，我们给出了最优攻击者和防御者策略的结构性质。我们提出了一个线性时间算法来计算的基础上的结构属性的值，这是一个改进，从我们以前的结果在\cite{emadi2019security}，特别是在大规模零和游戏的背景下。
英文摘要：
In this work, we investigate a security game between an attacker and a defender, originally proposed in \cite{emadi2019security}. As is well known, the combinatorial nature of security games leads to a large cost matrix. Therefore, computing the value and optimal strategy for the players becomes computationally expensive. In this work, we analyze a special class of zero-sum games in which the payoff matrix has a special structure which results from the {\it additive property} of the utility function. Based on variational principles, we present structural properties of optimal attacker as well as defender's strategy. We propose a linear-time algorithm to compute the value based on the structural properties, which is an improvement from our previous result in \cite{emadi2019security}, especially in the context of large-scale zero-sum games.
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