📚 Divisions between realism and liberalism: A Game Theory Approach | 现实主义与自由主义的分歧：博弈论视角
In international relations, the debate between realism and liberalism structures much of our understanding of state behaviour. However, at A-Level Decision Mathematics, we can use game theory to formalise these competing worldviews as distinct assumptions about strategic interaction, payoffs, and the possibility of cooperation. By modelling states as rational players in a game, the divisions between realism and liberalism become clearer and more analytically tractable.
在国际关系领域，现实主义与自由主义之间的争论构成了我们对国家行为理解的主线。然而，在A-Level决策数学中，我们可以借助博弈论将这两种对立的世界观形式化，将其视为对国家间战略互动、收益结构以及合作可能性所持的不同假设。将国家建模为博弈中的理性参与者，现实主义与自由主义的分歧就会变得更加清晰，也便于分析。
1. Core Assumptions of Realism: A Zero-Sum View | 现实主义的核心假设：零和博弈观
stem. In game-theoretic terms, this often translates into a zero-sum game, where one state's gain is exactly another state's loss. The total sum of payoffs remains constant, meaning that any improvement in a rival' erefore difficult to sustain because a relative gain for the opponent is seen as a threat.
现实主义者主张，国际政治是无政府体系下的权力斗争。用博弈论的语言来说，这常常被转化为零和博弈，即一个国家的收益恰好等于另一个国家的损失。收益总和保持不变，这意味着对手状况的任何改善都直接削弱了自身。对于现实主义者而言，国家A和国家B的收益P和Q始终满足 P + Q = 常数。因此，合作很难维持，因为对手的相对获益会被视为威胁。
In this view, the best strategy is self-help and maximisation of one's own power, akin to a minimax strategy in a two-player zero-sum game where each player seeks to minimise the opponent's maximum payoff. This leads to a permanent state of competition and mutual suspicion.
在这种观点下，最佳策略是自助和最大化自身权力，类似于两人零和博弈中的极小极大策略：每个参与者都试图最小化对手的最大收益。这导致了一种持久的竞争和相互猜忌的状态。
2. Core Assumptions of Liberalism: Positive-Sum Cooperation | 自由主义的核心假设：正和合作
Liberals, by contrast, view international relations as a domain where positive-sum games are possible. Through trade, institutions, and shared norms, states can achieve absolute gains where both parties benefit simultaneously. In a liberal framework, the payoff matrix is not zero-sum; instead, cooperative moves can increase the total pie. The utility functions UA and UB can both increase as a result of coordinated strategies.
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