网络国际关系中的纳什均衡寻求算法
Power Allocation Games on Signed Networks: Nash Equilibria and Coevolutionary Dynamics
AI总结：
本文提出一种用于网络国际关系中权力分配游戏的纳什均衡寻求算法，通过修改偏好公理和引入新算法，提升对国家战略互动的分析能力。
摘要：
在国际安全领域，理解国家在网络化背景下之间的战略互动至关重要。我们之前的研究引入了一个『在有向图上进行游戏』的框架~\cite{LiMorse2022}来分析这些互动。尽管该框架旨在基础且通用，但仍有许多待探索之处，特别是捕捉国际关系中战略场景的复杂性。本文旨在通过两种关键方式填补这一空白。首先，我们修改了现有的偏好公理，以更细致地理解国家如何追求自我生存、保护盟友和对敌人进攻。其次，我们引入了一种新的算法，证明了这些修改后的游戏中纯策略纳什均衡的存在。为了验证我们的模型，我们采用1940年的历史数据作为游戏输入，并预测国家的生存能力。我们的贡献因此扩展了原始框架在现实中的适用性，为网络化安全环境中的战略互动提供了更全面的视角。
英文摘要：
Understanding how strategic interactions and power distributions coevolve in international relations is central to explaining conflict, cooperation, and long-term inequality. We study this problem using a power-allocation game on signed networks. Departing from models that restrict strategy updates to Pareto improvements, we propose a generalized formulation in which countries prioritize self-survival and strategically trade off between supporting allies and weakening adversaries. This relaxation allows countries to sacrifice certain allies to achieve higher overall payoffs. For the resulting static game, we establish the existence of pure-strategy Nash equilibria and characterize their properties in extreme cases, including fully antagonistic networks and the presence of a dominant power. We further introduce a power-strategy coevolutionary dynamic and prove its almost-sure convergence to equilibria corresponding to the static game. The proposed models are validated using empirical data and numerical simulations. Historical data from the Correlates of War and national capability datasets show that survival likelihood predicts countries' safety outcomes and subsequent economic growth with relatively high accuracy. Simulations further indicate that, under fixed conflict intensity, more structurally balanced signed networks yield higher average power and lower inequality at steady states.
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