We develop an analytical Stackelberg game framework for optimal resource allocation in a sequential attacker--defender setting with a finite set of assets and probabilistic attacks. The defender commits to a mixed protection strategy, after which the attacker best-responds via backward induction. Closed-form expressions for equilibrium protection and attack strategies are derived for general numbers of assets and defensive resources. Necessary constraints on rewards and costs are established to ensure feasibility of the probability distributions. Three distinct payoff regimes for the defender are identified and analysed. An eight-asset numerical example illustrates the equilibrium structure and reveals a unique Pareto-dominant attack configuration.
翻译:本文构建了一个解析性斯塔克尔伯格博弈框架,用于在有限资产集合与概率性攻击的序贯攻防场景中进行最优资源分配。防御方首先承诺采用混合保护策略,随后攻击方通过逆向归纳法做出最优响应。我们针对任意数量的资产与防御资源,推导出均衡保护策略与攻击策略的闭式表达式。为确保概率分布的可行性,建立了关于收益与成本的必要约束条件。研究识别并分析了防御方的三种不同收益机制。通过一个包含八项资产的数值算例,阐明了均衡结构,并揭示了一种独特的帕累托占优攻击构型。