Acceptance that there is anarchy in the global system | 接受全球体系中的无政府状态：博弈论视角

📚 Acceptance that there is anarchy in the global system | 接受全球体系中的无政府状态：博弈论视角

In Edexcel A-Level Mathematics, especially in Decision Mathematics, game theory provides a formal framework for analysing interactions between rational agents when no central authority exists. The statement ‘there is anarchy in the global system’ can be modelled as a game with no external enforcer. This article explains how mathematical models help us accept and understand the consequences of global anarchy.

在 Edexcel A-Level 数学（尤其是决策数学）中，博弈论为分析没有中央权威时理性主体之间的互动提供了形式化框架。“全球体系存在无政府状态”这一命题可以建模为一个没有外部执行者的博弈。本文解释数学模型如何帮助我们接受并理解全球无政府状态所带来的后果。

1. Anarchy as absence of a central authority | 无政府状态：缺乏中央权威

In international relations, anarchy does not mean chaos or violence; it means the absence of a single global government that can enforce rules. From a mathematical modelling perspective, this is equivalent to a multi-player game with no external referee or binding contract mechanism.

在国际关系中，无政府状态并不意味着混乱或暴力，而是指不存在一个能够执行规则的单一全球政府。从数学建模角度看，这等价于一个没有外部裁判或具有约束力的合同机制的多主体博弈。

When states interact, they must rely on self-help and bilateral or multilateral agreements that are not perfectly enforceable. This creates strategic uncertainty that can be captured by non-cooperative game theory.

当国家互动时，它们必须依靠自助以及并非完全可执行的双方或多边协议。这产生了战略不确定性，可以用非合作博弈论来刻画。

2. Game theory basics: players, strategies, payoffs | 博弈论基础：局中人、策略与收益

A game in normal form consists of a set of players, a strategy set for each player, and payoff functions that assign numerical outcomes to every possible combination of strategies. In a global system, the players are states or other international actors.

标准式博弈由一组局中人、每个局中人的策略集以及收益函数组成，收益函数为每一种可能的策略组合赋予数值结果。在全球体系中，局中人就是国家或其他国际行为体。

Formally, a two-player game can be represented by a payoff matrix, where rows are Player 1’s strategies and columns are Player 2’s strategies. The game is written as:

形式上，双人博弈可以用一个收益矩阵表示，其中行代表局中人1的策略，列代表局中人2的策略。该博弈可以写成：

G = {N, S₁, S₂, u₁, u₂}

where N = {1, 2} is the set of players, Sᵢ is the strategy set of player i, and uᵢ is the payoff function of player i.

其中 N = {1, 2} 是局中人集合，Sᵢ 是局中人 i 的策略集，uᵢ 是局中人 i 的收益函数。

3. Prisoner’s Dilemma and the security dilemma | 囚徒困境与安全困境

The Prisoner’s Dilemma is a standard model of the security dilemma in an anarchic system. Two states can either cooperate (C) or defect (D). Mutual cooperation gives a good outcome, but each state has an incentive to defect to gain a short-term advantage.

囚徒困境是无政府体系中安全困境的标准模型。两个国家可以选择合作（C）或背叛（D）。相互合作会带来良好结果，但每个国家都有背叛以获取短期优势的动机。

Published by TutorHao | A-Level Mathematics Revision Series | aleveler.com

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