经济博弈论14

1 边缘政策：古巴导弹危机 Brinkmanship The Cuban Missile Crisis 第14章 Chapter 14 Slide 2 作为策略性行动的边缘政策：简要回顾 Brinkmanship as a Strategic Move: A quick Reminder 威胁是一种反应规则，威胁行动对发出威胁者和威胁 的针对者都造成成本。 A threat is a response rule, and the threatened action inflicts a cost on both the player making the threat and the player whose action the threat is intended to influence. 不过，如果威胁如愿以偿，该行动实际上不会被采用。 However, if the threat succeeds in its purpose, this action is not actually carried out. 因而威胁要采取的行动看起来并没有一个成本的上限。 Therefore there is no apparent upper limit to the cost of the threatened action. 2 Slide 3 作为策略性行动的边缘政策：简要回顾 Brinkmanship as a Strategic Move: A quick Reminder 不过出错的风险——威胁可能未能达到目的，或者威 胁要采取的行动意外发生了——迫使策略家采用能够 达到目的的最小威胁。 But the risk of errors – that is, the risk that the threat may fail to achieve its purpose or that the threatened action may occur by accident – forces strategist to use the minimal threat that achieve its purpose. 如果实践中找不到较小的威胁，一个大的威胁可以通 过将它的实施概率化来减弱效果。 If a smaller threat is not naturally available, a large threat can be scaled down by making its fulfillment probabilistic. Slide 4 作为策略性行动的边缘政策：简要回顾 Brinkmanship as a Strategic Move: A quick Reminder 因而你必须在事先就做出安排，使得事情在一 定程度上不在你控制之内。 Therefore you must arrange in advance to let things get out of your control to some extent. 边缘政策就是这样一种概率威胁的创造和使用。 Brinkmanship is the creation and deployment of such a probabilistic threat. 3 Slide 5 作为策略性行动的边缘政策：简要回顾 Brinkmanship as a Strategic Move: A quick Reminder 边缘政策是一个微妙和危险的策略。 Brinkmanship is a subtle and dangerous strategy. 许多商业与个人互动中的冲突——例如罢工、 关系破裂——都是边缘政策误入歧途的例子。 Many conflicts in business and personal interactions – such as strikes and breakups of relationships – are examples of brinkmanship gone wrong. Slide 6 边缘政策与古巴导弹危机 Brinkmanship and the Cuban Missile Crisis 我们将对1962年古巴导弹危机做一个充分的案例研究， 以说明这一概念。 We will use the Cuban Missile Crisis of 1962 as an extended case study to explicate the concept. 在这样的基于理论的案例研究中，特定案例的详细事 实将和博弈理论分析更为密切地结合，以达到对事实 及其原因的更充分的理解。 In such theory-based case studies, factual details of a particular case are more closely integrated with game-theoretic analysis to achieve a fuller understanding of what has happened and why. 4 Slide 7 内容提要 Outline 事件简述 A brief narration of events *一个简单的博弈理论解释 A Simple game-theoretic explanation *考虑额外的复杂性 Accounting for additional complexities *概率威胁 A probabilistic threat 实践边缘政策 Practicing brinkmanship Slide 8 事件简述 A Brief Narration of Events 1962年10月16日，美国发现苏联在古巴部署导弹。 On Oct 16, 1962, the USSR was found by the US to place missiles in Cuba. 10月22日，美国宣布封锁古巴并要求立即撤回导弹。 封锁于10月24日实施。 On Oct 22, the US announced a blockade and demanded a prompt withdrawal. The blockade went into effect on Oct 24. 10月26日，苏联两次提出与美国的交换条件，但渐趋 强硬。 On Oct 26, the USSR offered two (gradually hardened) deals to the US. 5 Slide 9 事件简述 A Brief Narration of Events 10月27日，美国提出强硬的条件，要求在12 －24小时内答复；否则“后果不堪设想”。 On Oct 27, the US made a tough offer, requiring an answer within 12 to 24 hours; otherwise “there would be drastic consequences”. 10月28日，苏联宣布撤出导弹。 On Oct 28, the USSR announced a withdrawal. Slide 10 一个简单的博弈论解释 A Simple Game-theoretic Explanation 美国想让苏联从古巴撤出导弹，因而其目标是 达到“强迫”。 The US wanted the USSR to withdraw its missiles from Cuba; thus the US objective was to achieve compellence. 为了这一目的，美国进行威胁：如果苏联不答 应，就会最终导致两个超级大国之间的核战争。 For this purpose, the US deployed a threat: Soviet failure to comply would eventually lead to a nuclear war between the superpowers. 6 Slide 11 一个简单的博弈论解释 A Simple Game-theoretic Explanation 封锁是这一不可避免的进程的起点，也是美国显示其 决心的可信性的一个实际行动。 The blockade was a starting point of this inevitable process and an actual action that demonstrated the credibility of US resolve. 只要威胁对于对手的成本足够大，迫使它按照我们所 希望的采取行动，那么我们就无论如何不会实施这一 结果很坏的行动。 All that is needed is that the threat be sufficiently costly to the other side to induce it to act in accordance with our wishes; then we don’t have to carry out the bad action anyway. Slide 12 危机的简单威胁模型 The Simple-Threat Model of the Crisis U.S. USSR Threaten Don’t Withdrawal Defy 1, -4 -10, -8 -2, 2 U.S., USSR 7 Slide 13 考虑额外的复杂性 Accounting for Additional Complexities 威胁的大小只需要有一个下限——足够 大以便吓退对手——的想法，只在做出 威胁者能够绝对保证每件事情都在掌控 之中时，才是正确的。 The idea that a threat has only a lower limit on its size –that it be large enough to frighten the opponent – is correct only if the threatener can be absolutely sure that everything will go as planned. Slide 14 考虑额外的复杂性 Accounting for Additional Complexities 但是，大多数博弈都有一定的不确定性。 But almost all games have some element of uncertainty. „ 你不能准确知道对手的价值评判。 You cannot know your opponent’s value system for sure. „ 你不能完全确定参与者想要实施的行动能够 被恰当地执行。 You cannot be completely sure that the players’ intended actions will be accurately implemented. 8 Slide 15 考虑额外的复杂性 Accounting for Additional Complexities 因而威胁具有双重风险。 Therefore a threat carries a twofold risk. „ 你的对手可能藐视它，这迫使你采取代价高昂的威胁行动； Your opponent may defy it, requiring you to carry out the costly threatened action; „ 你的对手可能顺从了，但威胁行动却错误地发生了。 Your opponent may comply, but the threatened action may occur by mistake anyway. 当这样的风险存在时，威胁行动对自身的成本必须加 以认真考虑。 When such risks exist, the cost of threatened action to oneself becomes an important consideration. Slide 16 考虑额外的复杂性 Accounting for Additional Complexities 古巴导弹危机充满了这样的不确定性。 The Cuban missile crisis was replete with such uncertainties. „ 双方都不能确知对方的收益——对方会如何看待战争与“丢脸” 的相对成本。 Neither side could be sure of the other’s payoffs – that is, of how serious the other regarded the relative costs of war and of losing prestige in the world. „ “封锁”与“空袭”的选择并不象字面上那么简单，在华盛顿或 莫斯科的命令与其远在大西洋上的古巴的执行之间存在许多 薄弱的联系和随机效应。 The choice of “blockade” and “air strike” were much more complex that the simple phrases suggest, and there were many weak links and random effects between an order in Washington or Moscow and its implementation in the Atlantic Ocean or in Cuba. 9 Slide 17 考虑额外的复杂性 Accounting for Additional Complexities 所有这些因素使得双方高层的任何决策的后果都难以 预料。 All these factors made the outcome of any decision by the top-level commander on each side somewhat unpredictable. 这就导致了“威胁出错”的很大的风险。 This gave rise to a substantial risk of the “threat going wrong”. 实际上，肯尼迪（时任美国总统）预测封锁导致战争 的几率在“三分之一与二分之一间。” In fact, Kennedy, the US president, thought that the chances of the blockade leading to war were “between one out of three and even”. Slide 18 考虑额外的复杂性 Accounting for Additional Complexities 这样的不确定性使得采取简单的威胁行动动作 过大而不能为威胁发出者所接受。 Such uncertainty can make a simple threat too large to be acceptable to the threatener. 我们考虑其中一种不确定性——美国不确知苏 联的真实意图。 We will take one particular form of the uncertainty – U.S. lack of knowledge of the Soviet’s true motives. 10 Slide 19 与强硬苏联的博弈 The Game with Hard-line Soviets U.S. USSR Threaten Don’t Withdrawal Defy 1, -8 -10, -4 -2, 2 U.S., USSR Slide 20 对收益未知的苏联采取威胁 The Threat with Unknown Soviet Payoffs U.S. USSR Threaten Don’t Withdrawal Defy 1, -8 -10, -4 -2, 2 U.S., USSR U.S. USSR Threaten Don’t Withdrawal Defy 1, -4 -10, -8 -2, 2 Nature Soviet’s Hard-line (prob. p) Soviet’s soft (prob. 1-p) 11 Slide 21 对收益未知的苏联采取威胁 The Threat with Unknown Soviet Payoffs 如果采取威胁的期望收益大于不采取威胁，美国就采 取威胁。即： The U.S. should make the threat if the expected payoffs from making the threat is larger than not, that is, -10p+(1-p)>-2, or p<3/11=0.27 实际上，肯尼迪预测的p值不满足该条件： On this instance, Kennedy’s estimate of p did not satisfy this condition: 3/11<1/3

0.6. 我们称概率q的这一下限为有效性条件。 We call this lower bound on the probability q the effectiveness condition. Slide 28 危机的边缘政策模型 The Brinkmanship Model of the Crisis 注意，对于美国来说，一个无效的威胁绝不比 完全没有威胁更好。因为： Notice that for the U.S., an noneffective threat cannot be better than no threat at all. Since, -2-8q≤-2, for any q∈[0,1] 还要注意，强硬型苏联肯定会拒绝边缘政策的 威胁。因为： Notice also that the hard-line Soviets will definitely defy the brinkmanship threat. Since, 2-6q>-8, for any q∈[0,1] 15 Slide 29 危机的边缘政策模型 The Brinkmanship Model of the Crisis 假定威胁对软弱型苏联有效，则美国来自这一 概率威胁的期望收益为： The expected payoff to the U.S. from the probabilistic threat, assuming that it is effective against the soft-type Soviets, is (-2-8q)×p+1×(1-p)=-8pq-3p+1. 因而美国采取这一威胁的条件是： Therefore the condition for the United States to make the threat is, -8pq-3p+1>-2, or q<(3/8)(1-p)/p Slide 30 危机的边缘政策模型 The Brinkmanship Model of the Crisis 也就是说，战争的概率必须足够小（满足该表达 式），否则美国将根本不采取威胁。我们称这一q 值的上限为可接受性条件。 That is, the probability of war must small enough to satisfy this expression or the U.S. will not make the threat at all. We call this upper bound on q the acceptability condition. 对于满足这一条件的q值，q值越小对美国越好 （不过好处可能不明显）。 For q satisfying such a condition, the smaller the q, the better off the U.S.. (But this scale-down effect may not be significant.) 16 Slide 31 危机的边缘政策模型 The Brinkmanship Model of the Crisis 要想使概率威胁起作用，它就必须同时 满足有效性和可接受性条件。 If the probabilistic threat is to work, it should satisfy both the effective and the acceptability condition. Slide 32 成功的边缘政策的条件 Conditions of Successful Brinkmanship 1 0.6 q p10.27 0.38 Zone where both conditions hold Lower limit (effectiveness condition) Upper limit (acceptability condition) If p<0.38, U.S.’s best choice is q*=0.6. If p>0.38, U.S.’s best choice is q*=0, or no threaten. 17 Slide 33 Suppose US estimated that: 1/30.38, then q*=0. US concedes and USSR wins. Slide 34 实践边缘政策 Practicing Brinkmanship 因而在实际中的边缘政策是逐步提高相互损害 的风险。 Thus the brinkmanship in practice is the gradual escalation of the risk of mutual harm. „ 这可以用实时的小鸡博弈来形象说明。 It can be visualized vividly as chicken in real time. 不过，实际发生的相互损害的结果并不完全在 威胁发出者的控制之下。 However, the actual occurrence of the harmful outcome is not totally within the threatener’s control. 18 Slide 35 实践边缘政策 Practicing Brinkmanship 一旦出现并稳步增加的共同的灾难风险，不会在 美国还在摸索采取风险更大的军事选择的范围时， 突然实现了。 The ever-present and steadily increasing mutual risk of disaster does not come to pass as US is groping through the range of ever more risky military options. 这一持续上升的糟糕后果的风险使得边缘政策成 为如此微妙和危险的策略。 This continuing and rising risk of a very bad outcome is what makes brinkmanship such a delicate and dangerous strategy. Slide 36 实践边缘政策 Practicing Brinkmanship 如果在你增加风险程度时，你的对手顺从了， 你必须能够“扭转乾坤”——立即减少风险，迅 速地将其化解。 If, as you are increasing the level of risk, your opponent does comply, you must be able to “go into reverse” – begin reducing the risk immediately and quite quickly remove it from the picture. 这正是你威胁的隐含承诺要求你做的。 That is what your implicit promise of a threat asks you to do. 19 Slide 37 实践边缘政策 Practicing Brinkmanship 边缘政策无处不在 Brinkmanship is everywhere…… „ 企业与工会 A company vs. a labor union „ 丈夫与妻子，父母与孩子 A husband vs. a wife, or a parent vs. a child „ 总统与国会 The President vs. Congress „ 大陆与台湾 Mainland China vs. Taiwan Slide 38

Summary 在某些情况下，威胁策略下犯错误的风险，要 求使用尽可能小的威胁。 In some game situations, the risk of error in the presence of a threat may call for the use of as small a threat as possible. 当大的威胁不能采取其他方式建议削弱时，它 可以通过将其实施概率化来削弱。 When a large threat cannot be reduced in other way, it can be scaled down by making its fulfillment probabilistic. 20 Slide 39 总结 Summary 概率威胁的策略性使用（你将对手和自己暴露 在上升的损害风险之下）称为边缘政策。 Strategic use of probabilistic threat, in which you expose your rival and yourself to an increasing risk of harm, is called brinkmanship. 边缘政策要求参与者在不完全丧失控制的情况 下，放弃对博弈结果的控制。 Brinkmanship requires a player to relinquish control over the outcome of the game without completely losing control. Slide 40 总结 Summary 你必须创造一个具有某种风险程度的威胁，它 足够大到能强迫或阻止对手，足够小到对你来 说是可接受的。 You must create a threat with a risk level that is both large enough to be effective in compelling or deterring your rival and small enough to be acceptable to you. 为此，你必须通过逐步升高的相互损害来确定 双方可接受的风险程度。 To do so, you must determine the level of risk tolerance of both players through a gradual escalation of mutual harm.