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，理解国家在网络化背景下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。尽管该框架力求基础性与普适性，仍有诸多问题亟待探索，尤其是在刻画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，我们修正了现有的偏好公理，以更细致地刻画国家追求自我生存、防卫盟友及攻击对手的行为逻辑；其次，我们提出一种新颖算法，证明了修正后博弈存在纯策略纳什均衡。为验证模型，我们采用1940年的历史数据作为博弈输入，预测各国的生存概率。本研究的贡献在于拓展了原框架的现实适用性，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。