爱思英语编者按:博弈论又被称为对策论(Game Theory)既是现代数学的一个新分支,也是运筹学的一个重要学科。

博弈论主要研究公式化了的激励结构间的相互作用。是研究具有斗争或竞争性质现象的数学理论和方法。 博弈论考虑游戏中的个体的预测行为和实际行为,并研究它们的优化策略。生物学家使用博弈理论来理解和预测进化论的某些结果。
War games
战争博弈

A big pay-off for two game theorists
给两位博弈论专家的大奖
 
THIS year's Nobel prize for economics might almost have doubled as the prize for peace. On October 10th, three days after the International Atomic Energy Agency and its director-general, Mohamed ElBaradei, won their laurels for monitoring the misuse of nuclear power, the economics prize was bestowed on two scholars whose best work was also done in the shadow of the mushroom cloud.
 
今年的诺贝尔经济学奖几乎身兼了和平奖的角色。10月10日,也就是国际原子能机构及其总干事穆罕默德·埃尔-巴拉迪因为监控核能的错误使用而获奖三天后,经济学奖被授予了两位其最佳研究也是在蘑菇云阴影下完成的学者。
 
Robert Aumann, of Hebrew University, and Thomas Schelling, of the University of Maryland, are both game theorists. Game theory is now part of every economist's toolkit and has been recognised by the Nobel award before, when John Harsanyi, John Nash and Reinhard Selten shared the honour in 1994. It is the study of what happens when the calculating, self-interested protagonist of economic fable meets another member of his kind. In such encounters, neither party can decide what to do without taking into account the actions of the other.
 
希伯来大学的罗伯特·奥曼(Robert  Aumann)与马里兰大学的托马斯·谢林(Thomas Schelling)都是博弈论专家。博弈论现在是每一位经济学家工具箱的一部分,并且之前——即约翰·海萨尼(John Harsanyi)、约翰·纳什(John Nash)和赖因哈德·泽尔腾(Reinhard Selten)在1994年分享这个奖项时——曾获得过诺奖的承认。它是有关经济学故事中的爱算计并且以自我利益为中心的主角与另一个同类型的人相遇时会发生什么的研究。在这样的相遇中,双方之中的任何一方都不可能在不考虑另一方行为的前提下决定做什么。
 
During the cold war, two protagonists that captured game theorists' imaginations were the United States and the Soviet Union. How each of these nuclear adversaries might successfully deter the other was the most pressing question hanging over Mr Schelling's classic work, “The Strategy of Conflict”, published in 1960. The book ranged freely and widely in search of an answer, finding inspiration in gun duels in the Old West, a child's game of brinkmanship with its parents, or the safety precautions of ancient despots, who made a habit of drinking from the same cup as any rival who might want to poison them.
 
冷战期间,抓住了博弈论专家想象力的两个主角是美国和苏联。这两位核对手如何才能成功地震慑对方是悬在1960年出版的谢林的经典著作《 冲突的战略》(The Strategy of Conflict)中的最紧迫的问题。在寻找答案中,该书天马行空、旁征博引,在老西部的手枪决斗中、在孩子与父母的一种边缘博弈中、在由于可能想要毒死他们的对手而养成了从同一个杯子中喝酒的习惯的古代帝王的安全措施中寻找灵感。
 
Mr Schelling's back-of-the-envelope logic reached many striking conclusions that appeared obvious only after he had made them clear. He argued that a country's best safeguard against nuclear war was to protect its weapons, not its people. A country that thinks it can withstand a nuclear war is more likely to start one. Better to show your enemy you can hit back after a strike, than to show him you can survive one. Mr Schelling invested his hopes for peace not in arms reductions or fall-out shelters but in preserving the ability to retaliate, for example by putting missiles into submarines.
 
谢林的这种简单而有效的逻辑得出了许多只有在他揭示出来之后才显得是显而易见的惊人结论。他指出,国家之于核战争的最佳防范措施是保护自己的武器,而不是民众。认为自己能够经受住一场核战争的国家更有可能打响一场核战争。向敌人表明你能够在遭袭后做出反击,要好于告诉敌人你能够在一场核战争后存活下来。谢林没有把他和平的希望寄托在武器消减或核尘埃避难所上面,而不是寄托在了通过将导弹装入潜艇等方式以保存能力进行报复上面。
 
All-out thermonuclear warfare is the kind of game you get to play only once. Other games, however, are replayed again and again. It is these that fascinate Mr Aumann. In a repeated encounter, one player can always punish the other for something he did in the past. The prospect of vengeful retaliation, Mr Aumann showed, opens up many opportunities for amicable co-operation. One player will collaborate with another only because he knows that if he is cheated today, he can punish the cheat tomorrow.
 
全面核战争是那种只能进行一次的博弈。然而,其他的博弈却可以一次又一次地反复进行。吸引奥曼的正是这些博弈。在某种被重复多次的相遇中,一方总是能够因为另一方过去的所作所为而对其进行惩罚。奥曼指出,以牙还牙的复仇前景开启的是众多友好合作的机遇。一方只有在知道倘若自己今天上当受骗、明天就能惩罚这种欺骗行为的前提下才会与另一方合作。
 
Mutually assured co-operation
得到相互确认的合作
 
According to this view, co-operation need not rely on good will, good faith, or an outside referee. It can emerge out of nothing more than the cold calculation of self-interest. This is in many ways a hopeful result: opportunists can hold each other in check. Mr Aumann named this insight the “folk theorem” (like many folk songs, the theorem has no original author, though many have embellished it). In 1959, he generalised it to games between many players, some of whom might gang up on the rest.
 
根据这种观点,合作不必依赖于善意、诚信或者是外部协调。它只能出自对自身利益的冷静考量。这在许多方面是一个充满希望的结果:机会主义者能够保持相互制衡。奥曼将这种洞见称之为“无名氏原理” ( Folk theorem )(如同许多民谣一样,这个原理没有原创者,但是,许多人都对其有所贡献)。1959年,他将其归纳为其中的部分参与方可能抱团对付其他参与方的多方博弈。
 
Mr Aumann is loyal to a method—game theory—not to the subject matter of economics per se. His primary affiliation is to his university's delightfully named Centre for Rationality, not its economics department. Trained as a mathematician, he started out as a purist—pursuing maths for maths' sake—but soon found his work pressed into practical use. Between 1965 and 1968, for example, he co-wrote a series of reports for the United States Arms Control and Disarmament Agency. The Russians and Americans were pursuing gradual, step-by-step disarmament. But the military capabilities of each superpower were so shrouded in mystery that neither side knew precisely what game they were playing: they did not know what their opponents were prepared to sacrifice, nor what they themselves stood to gain. Without knowing how many missiles the Russians had, for example, the Americans could not know whether an agreement to scrap 100 of them was meaningful or not.
 
奥曼是忠诚于一种方法论——博弈论——而不是经济学本身的主题。他的主要隶属关系是对他的大学的名为理性中心而言,而不是对它的经济系而言。鉴于作为一位数学家所受的训练,他刚出道的时候是一位纯粹主义者——为了数学而数学。但是,不久,他就发现他的研究集中到了实用上面。例如,在1965年到1968年期间,他曾与别人合作,为美国军控与裁军机构撰写了一些列报告。当时,俄美两国正在寻求循序渐进的裁军。但是,两个超级大国的军事能力都被笼罩在神秘之中,以至于哪一方都不能确切地知道他们当时正在进行何种博弈:他们既不知道对手已经准备好牺牲什么,也不知道自己能得到什么。例如,由于不知道俄国人到底有多少导弹,美国人不可能知道一份砍掉其中100枚导弹的协议是否有意义。
 
In such games, Mr Aumann pointed out, how a player acts can reveal what he knows. If Russia were quick to agree to cut 100 missiles, it might suggest its missile stocks were larger than the Americans had guessed. Or perhaps the Russians just wanted the Americans to think that. Examples of such deception are not limited to the cold war. Some have speculated that Saddam Hussein pursued a similar strategy in the run-up to the invasion of Iraq in 2003. Despite apparently having no actual weapons of mass destruction left, he offered only the most grudging co-operation to weapons inspectors. The Iraqi dictator perhaps wanted to conceal the humiliating fact that he had nothing much to hide.
 
奥曼指出,在这种博弈中,一方如何行动能够揭示他知道什么。如果俄国人很快就同意消减100枚导弹,这可能意味着他们导弹的存量大于美国人的猜测。或者,这也可能是俄国人就是想让美国人有这种想法。这种欺骗的实例不局限于冷战。有人指出,萨达姆在美国于2003年入侵伊拉克之前一直在追求一种类似的策略。尽管显然没有任何实际的大规模杀伤性武器留下来,他仅对武器核查者提供了最勉强的合作。这位伊拉克独裁者或许是想掩盖他没有什么想要隐藏这个令人尴尬的事实。
 
Messrs Aumann and Schelling have never worked together, perhaps because the division of labour between them is so clear. Mr Aumann is happiest proving theorems; Mr Schelling delights in applying them. Mr Aumann operates at the highest levels of abstraction, where the air is thin but the views are panoramic. Mr Schelling tills the lower-lying valleys, discovering the most fertile fields of application and plucking the juiciest examples.
 
也许是由于两人间的分工明确,奥曼与谢林从未合作过。奥曼的幸福在于证明理论;谢林的兴趣在于应用这些理论。奥曼是在空气稀薄但视野开阔的抽象的最高层次运作;谢林是在低处的山谷中耕耘,发现了最肥沃的应用之地并且摘下了最丰硕的实例。
 
In one of his more unusual papers, Mr Aumann uses game theory to shed light on an obscure passage in the Talmud, which explains how to divide an asset, such as a fine garment, between competing claimants. You should give three-quarters to the person who claims all of it, and the remaining quarter to the person who claims half of it, the text instructs, somewhat inscrutably. Fortunately, the Nobel committee had no need for such a complicated rule in dividing up its prize. Between its two equally deserving laureates, it split the SKr10m ($1.3m) fifty-fifty.
 
在他的一篇更加不同寻常的论文中,奥曼利用博弈论阐释了《犹太法典》中的一段解释如何在竞争对手间分割一件华服之类的资产的晦涩文章。这段文章有点故作神秘的建议道,人们应当把这件华服的四分之三分给宣称全部拥有它那个人,把剩下的四分之一分给宣称拥有其一半的那个人。幸运的是,诺奖评委会对一个如此复杂的分配奖金的规则没有任何需要。在两位赢得相等的得主之间,它均分了100万瑞典克朗。