Strategic game models of defense against stealthy, targeted attacks that cannot be prevented but only mitigated are the subject of a significant body of recent research, often in the context of advanced persistent threats (APTs). In these game models, the timing of attack and defense moves plays a central role. A common assumption, in this literature, is that players are indifferent between costs and gains now and those in the distant future, which conflicts with the widely accepted treatment of intertemporal choice across economic contexts. This article investigates the significance of this assumption by studying changes in optimal player behavior when introducing time discounting. Specifically, we adapt a popular model in the games of timing literature, the FlipIt model, by allowing for exponential discounting of gains and costs over time. We investigate changes of best responses and the location of Nash equilibria through analysis of two well-known classes of player strategies: those where the time between players’ moves is constant, and a second class where the time between players’ moves is stochastic and exponentially distributed. By introducing time discounting in the framework of games of timing, we increase its level of realism as well as applicability to organizational security management, which is in dire need of sound theoretic work to respond to sophisticated, stealthy attack vectors.

中文翻译：

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时间安全博弈中的指数贴现

防御无法预防但只能缓解的隐秘、有针对性的攻击的战略博弈模型是近期大量研究的主题，通常是在高级持续威胁 (APT) 的背景下。在这些游戏模型中，攻击和防御动作的时机起着核心作用。在该文献中，一个常见的假设是参与者对现在和遥远未来的成本和收益漠不关心，这与在经济背景下广泛接受的跨期选择处理相冲突。本文通过研究引入时间折扣时最佳玩家行为的变化来研究这一假设的重要性。具体来说，我们采用了计时文学游戏中的一个流行模型，即 FlipIt 模型，它允许收益和成本随时间呈指数折扣。我们通过分析两类众所周知的玩家策略来研究最佳响应的变化和纳什均衡的位置：玩家移动之间的时间是恒定的，以及玩家移动之间的时间是随机的和指数级的。分散式。通过在时间游戏的框架中引入时间折扣，我们提高了其现实性水平以及对组织安全管理的适用性，这迫切需要可靠的理论工作来应对复杂、隐秘的攻击向量。第二类，玩家移动之间的时间是随机的并且呈指数分布。通过在时间游戏的框架中引入时间折扣，我们提高了其现实性水平以及对组织安全管理的适用性，这迫切需要可靠的理论工作来应对复杂、隐秘的攻击向量。第二类，玩家移动之间的时间是随机的并且呈指数分布。通过在时间游戏的框架中引入时间折扣，我们提高了其现实性水平以及对组织安全管理的适用性，这迫切需要可靠的理论工作来应对复杂、隐秘的攻击向量。