In the field of international security, understanding the strategic interactions between countries within a networked context is crucial. Our previous research has introduced a ``games-on-signed graphs'' framework~\cite{LiMorse2022} to analyze these interactions. While the framework is intended to be basic and general, there is much left to be explored, particularly in capturing the complexity of strategic scenarios in international relations. Our paper aims to fill this gap in two key ways. First, we modify the existing preference axioms to allow for a more nuanced understanding of how countries pursue self-survival, defense of allies, and offense toward adversaries. Second, we introduce a novel algorithm that proves the existence of a pure-strategy Nash equilibrium for these revised games. To validate our model, we employ historical data from the year 1940 as the game input and predict countries' survivability. Our contributions thus extend the real-world applicability of the original framework, offering a more comprehensive view of strategic interactions in a networked security environment.

翻译：在国际安全领域，理解网络化背景下国家间的战略互动至关重要。我们先前的研究引入了“符号图博弈”框架（LiMorse2022）来分析这些互动。虽然该框架设计为基础且通用的模型，但仍有许多方面有待探索，尤其是在捕捉国际关系中复杂战略场景方面。本文旨在通过两个关键方向填补这一空白：首先，我们修改了现有的偏好公理，以更细致地刻画国家追求自身生存、防御盟友及攻击对手的行为模式；其次，我们提出了一种新颖算法，证明了修正后博弈存在纯策略纳什均衡。为验证模型有效性，我们采用1940年的历史数据作为博弈输入，预测了各国的生存概率。本研究通过增强原始框架的现实适用性，为网络化安全环境中的战略互动提供了更全面的分析视角。