消弭核战的博弈论

How an economic theory beat the atomic bomb

The most important event of the second half of the 20th century is one that didn't happen." With those words, Thomas Schelling marked the "stunning achievement" of 50 years without a nuclear war. No one person can claim credit but Mr Schelling has as much claim as anyone to helping prevent Armageddon. He helped to prevent war because he understood it and explained it brilliantly to others, changing the intellectual climate, inspiring a generation of strategic thinkers and, almost incidentally, saving the young discipline of game theory from irrelevance.


On Monday, Mr Schelling shared the Nobel Prize in Economics with Robert Aumann, the mathematician. The prize is long overdue but also a curious reward for a man who did almost no research as such. "If you ask what he does for a living, I have to answer that he lives by his wits," James Coleman, the sociologist, once remarked.

If you want to win a Nobel Prize without doing technical research, Mr Schelling's winning formula is simple: find hidden patterns or puzzles of everyday life that no one else can see, show how they illuminate the biggest questions of the day and write it all up in the most sparkling prose.

Game theory was - before Mr Schelling - the mathematical analysis of interdependent decisions: whether a union calls a strike depends on whether the union leaders think the management will respond with a better pay offer; whether I bluff at poker depends on whether I think you are likely to call the bluff. Game theory and the atomic bomb arrived at the same time with the help of the same mathematician, John von Neumann, and the early game theorists tried to use the theory to understand nuclear war. But their analysis was weak. Von Neumann told Life magazine: "If you say why not bomb them tomorrow, I say why not today?"

Mr Schelling's 1960 book, TheStrategy of Conflict, revolutionised both strategic thinking and game theory. Mr Schelling ditched the mathematics of his peers and applied the rigorous thinking of game theory to a richer world in which the superpowers tried to understand the tacit signals behind each others' threats and promises. He showed that even the deadliest wars involved significant elements of common interest and co-operation between foes. Indeed, the striking fact that the cold war never became a hot one is the co-operative feat of the century.

Alfred Marshall, the great economist, advised other economists to translate their mathematics into plain English and illustrate it with real-life examples. We have largely ignored his advice, but Mr Schelling lives it. Explaining the difference between stable and unstable deterrence, he imagined a face-off in the wild west, with both men on a hair-trigger, before observing: "If both were assured of living long enough to shoot back with unimpaired aim, there would be no advantage in jumping the gun and little reason to fear that the other would try it." Such thinking helped to change the US's stated policy of massive retaliation for any Soviet transgression in favour of maintaining a credible second-strike capability to discourage a surprise attack. The resulting face-off did indeed prove more stable than anyone dared to hope.

Mr Schelling's leaps of lateral thinking have been so spectacular that his colleagues sometimes thought he had lost his mind. On a long flight, his doodles with noughts and crosses convinced him that the extreme racial segregation often seen in modern cities could arise without extreme racial prejudice. As some families try to avoid being surrounded by a different ethnic group, sharp boundaries can arise in a city full of people who are content with genuinely mixed neighbourhoods. The outcome is out of all proportion to the motives that produce it. Thirty years later, Mr Schelling's method was being fed into powerful computers and became a cutting-edge research topic - agent-based modelling.

Nor is Mr Schelling limited to matters of solemn policy: he has studied efficient ways for criminal gangs to extort money, the problem of ever-expanding Christmas card lists and how to find a travelling companion after being separated in a strange city. That eclectic mix is inseparable from his ability to find wisdom in unusual analogies.

Mr Schelling is a great communicator of economic ideas; many would say he is the great communicator. I only wish that more economists would imitate his methods. Our only defence is that he is inimitable.
消弭核战的博弈论



“20世纪后50年最重要的事件是有一件事情没有发生。” 托马斯?谢林（Thomas Schelling）的这句话，指的是50年没有爆发核战争这一“非凡的成就”。

这一成就不能归功于哪一个人，但在帮助避免世界末日的大决战（核战争）方面，谢林先生的贡献不逊于任何人。之所以说他为避免战争作出了贡献，是因为他对战争有着透彻的理解，并作出了精辟的阐释，是他改变了知识潮流，影响了一代战略思想家，同时，几乎是在无意之间，使诞生初期的博弈论学科不至纠缠于细枝末节。


本周一，谢林与数学家罗伯特?奥曼（Robert Aumann）分享了诺贝尔经济学奖。这一奖项姗姗来迟，但将它颁发给谢林先生这样一位几乎不从事研究的学者，也有些令人纳罕。社会学家詹姆斯?科尔曼（James Coleman）曾说过这样的话：“如果你们要问他何以谋生，我只能这样回答：凭借他的智慧。”

如果你也想不作什么技术研究就赢得诺贝尔奖的话，谢林先生的成功秘诀其实很简单：去发现隐藏在日常生活中别人没能总结出来的方法或思路，展示如何利用它们说明当时最重大的问题，并用最绚丽的笔法加以详尽阐述。

在谢林先生之前，博弈论是对相互影响的结果进行数学分析――工会是否号召罢工，取决于工会领袖是否认为管理层会因此给工人加薪；我是否会在打扑克牌时作弊，取决于我是否觉得你有可能识破这一伎俩。博弈论和原子弹几乎同时诞生，都得益于同一位数学家：约翰?冯?诺伊曼（John von Neumann），早期的博弈论理论家曾试图用这一理论来理解核战争。但当时他们的分析缺乏说服力。诺伊曼就曾经向《生活》(Life)杂志表示：“如果你问为什么不在明天轰炸敌人，那我要说，为什么不是今天呢？”

谢林1960年出版的《冲突的战略》(The Strategy of Conflict)一书，使战略思想和博弈论都发生了根本性的改变。谢林摒弃了同行们的数学方法，将博弈论的严谨思想应用于更为丰富的世界――在这个世界中，超级大国们力图理解对方威胁与承诺背后，彼此心照不宣的信号。谢林指出，即使是再不共戴天的战争，也包含着敌对双方共同利益与合作的重要因素。实际上，冷战一直没有演变成真枪实战这一惊人的事实，正是20世纪各方合作的结果。

伟大的经济学家阿尔弗雷德?马歇尔(Alfred Marshall)曾建言其他经济学家，将他们的数学理论转化成通俗易懂的语言，并用现实生活中的例子加以阐述。我们往往忽略了马歇尔的建议，但是谢林却身体力行。

为了解释稳定威慑与非稳定威慑之间的差别，谢林设想出一幕开拓西部时的对峙场景，对峙双方弹在膛中，一触即发。然后他评论道：“如果双方都确信自己有把握在临死之前进行准确的还击，那么先开枪的一方将无任何优势可言，这样也就无须害怕对方会先开枪。”

美国一改对苏联侵犯实施大规模报复的既定政策，转而采取保持可靠的二次打击能力以避免对方突袭的策略，这中间上述思想起到了一定作用。结果表明，这种对峙的稳定程度之高，超出了所有人的想象。

谢林先生的横向思维极富跳跃性，以至于他的同事们有时认为他脑子出了问题。在一次长途飞行中，他在信手圈圈点点之后发现，即使没有极端的种族歧视，现代城市中常见的极端种族隔离现象也可能出现。当一些家庭试图避免被一个不同种族的群体所包围时，在一个人们都满足于不同种族真正混居的城市里，也可能出现鲜明的界线。这种事态结果与其产生的动机大相径庭。30年后，谢林先生的方法论被输入功能强大的电脑系统，并成为一项最前沿的研究课题――基于代表性主体的 (agent-based modelling)建模。

谢林先生也不曾把自己局限于严肃的政策问题：他曾研究犯罪团伙勒索钱财的有效途径、圣诞贺卡联系人名单不断拉长的问题，以及在陌生城市如何找到失散的旅伴。这些古怪的论题，与他那种通过不寻常的类推中发现真谛的能力密不可分。

谢林先生是经济学思想的一位伟大交流者；许多人也认为如此。我只是希望更多的经济学家能效仿他的方法。唯一的原因在于：他本人是无法效仿的。

作者为《金融时报》撰写《亲爱的经济学家》专栏，他还著有《卧底经济学家》(The Undercover Economist)一书，该书将于11月由牛津大学出版社出版。

博弈论学者荣膺本届诺贝尔经济学奖
Economic Work On 'Game Theory' Wins Nobel Prize

The Cold War was a period of conflict management on a grand, frightening scale, and two researchers who explained how individuals negotiate such conflict won the Nobel prize in economics for work that grew out of the period.


Thomas Schelling, an 84-year-old retired University of Maryland professor who served long stints as an adviser to the U.S. government, has written on managing the U.S.-Soviet buildup of nuclear arms and extended his theories to subjects such as drug addiction, racial segregation and global warming. Robert Aumann, 75, a mathematician by training and professor at Hebrew University in Jerusalem, added analytical rigor to the field that both professors helped to create, which has come to be known in economics as "game theory."

The two will share the 10 million kronor prize ($1.3 million) awarded by the Royal Swedish Academy of Sciences. Mr. Schelling is an American citizen, and Mr. Aumann is an American and Israeli citizen.

Game theory is the study of strategy and how people make decisions when interacting in conflict with one another. In a game of chess, two players act not only based on their own strategy, but also on expectations of how their opponent will behave and react. In the 1940s and 1950s, economists began to see their models of individual behavior needed to be less robotic and should reflect the kind of strategic dance found in games like chess.

The movement toward game theory was driven in part by mathematicians like Mr. Aumann and an associate from his days at the Massachusetts Institute of Technology named John Nash, whose life was portrayed in the movie "A Beautiful Mind." Mr. Nash won the economics prize with two others in 1994.

While Messrs. Nash and Aumann used math to give precise formulations to game theory, Prof. Schelling sought to give it practical meaning. He explained, for instance, how decision makers often find it advantageous to limit their own options to get concessions from an opponent. In some cases, for instance, it might be wise for a general to burn bridges behind his troops to send a credible and possibly game-changing message toward his enemy that he has no intention of retreating.


Economists have since applied this idea of "precommitment" to other areas, including business. Some companies, for example, might find it advantageous to build too much capacity, to alert would-be competitors that entering a market will lead them into a price war.

"Schelling classified and explained the ways that strategic moves operate," said Avinash Dixit, a Princeton University professor. Mr. Dixit said the award for Mr. Schelling was long overdue. "I have been hoping for this for the past 15 or 20 years."

Messrs. Schelling and Aumann both came of age during the Cold War, when fears of a nuclear confrontation between the Soviet Union and the U.S. led scholars to examine the motivations and decision-making of both sides. Mr. Schelling's career began with work on the Marshall Plan to help rebuild Europe after World War II.

Prof. Aumann, whose family fled Nazi Germany in 1938, considered becoming a scholar of the Jewish Talmud before turning to mathematics. He says he was drawn to game theory shortly after earning his Ph.D., when he moved to Princeton University and took part in research to lay out defense strategies for a hypothetical city being attacked by a squadron of airplanes. He moved to Israel from the U.S. in the 1950s.

Prof. Schelling extended his research beyond the Cold War. For instance, his work has shown how even small differences in preferences between groups of people could lead to large-scale segregation in cities. It also has described drug addiction as a game against oneself. Someone who is trying to quit smoking, for instance, might flush cigarettes down the toilet because he realizes that "some time late at night he won't be able to resist them."

The economics prize is the only Nobel not established in the will of Alfred Nobel, the inventor of dynamite. It was set up separately in 1968 and is called "Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel."
博弈论学者荣膺本届诺贝尔经济学奖



冷战可谓一场规模宏大惊心动魄的冲突管理，在此基础上进行理论研究，揭示个人在冲突期间如何沟通互动的两位经济学家夺得了本年度诺贝尔经济学奖。

现年84岁的托马斯?谢林(Thomas Schelling)是马里兰大学(University of Maryland)退休教授，曾长期担任美国政府顾问。他就美苏核武扩军管理的主题撰写了大量文章，并将他的理论扩展到吸毒、种族隔离和全球气候变暖等领域。罗伯特?奥曼(Robert Aumann)现年75岁，这位受过专业训练的数学家后来到位于耶路撒冷的希伯莱大学(Hebrew University)作教授，他为谢林和自己开创的这片领域增添了严格的学术分析色彩，这就是后来在经济学研究中颇负盛名的“博弈论”。

两位学者将分享瑞典皇家科学院(Royal Swedish Academy of Sciences)颁发的1,000万克朗（130万美元）奖金。谢林是美国公民，奥曼持有美国和以色列双重国籍。

博弈论研究的是战略，讨论人们在冲突中如何互动怎样决策。对弈的两名棋手不但根据自己的思路，还要考虑到对手可能做出的反应来决定落子。四、五十年代，经济学家们开始探索个人行为方式的模型，认为这个模型应该少些机械性，要能够反映棋类游戏中对抗双方的战略互动。

博弈论研究的动力部分来自奥曼等数学家，以及奥曼在麻省理工大学(Massachusetts Institute of Technology)的同事约翰?纳什(John Nash)。纳什的人生悲喜后来被拍成一部电影《美丽人生》(A Beautiful Mind)。他在1994年与另外两位学者同获诺贝尔经济学奖。

纳什和奥曼等人用数学分析给博弈论列出精确的公式，谢林则另辟蹊径，试图给博弈论添加实践意义。例如，谢林就利用博弈论解释，决策者怎样经常找到缩小自己行动选择从而得到对手妥协的优势。又比如，很多时候，军队将领下令烧毁背后的桥梁，由此向对手发出一条可信的、同时也很有可能改变战局的消息：我方无意撤退。

此后，经济学家们就开始在其他领域使用这种“先验承诺”的观点，也包括商业范畴。例如，有些公司可能会发现兴建大量、未免过剩的产能这种做法会有利可图，因为它向准备入行的公司发出的信息是：一旦闯进来就要准备打一场价格战。

普林斯顿大学(Princeton University)教授阿维纳什?迪克西特(Avinash Dixit)说，谢林分类整理并解释了战略行动的奏效原理。他说谢林早就该获得这个奖项了，“我期待这一天已经有15年到20年了。”

谢林和奥曼都在冷战时期度过了人生的盛年。对美苏两国爆发核冲突的恐惧促使学者们纷纷研究双方的动机和决策。谢林的研究就始于二战后帮助重建欧洲的马歇尔计划(Marshall Plan)。

奥曼的家人1938年逃离纳粹德国，他曾经想专门研究犹太教经典《塔木德经》(Talmud)，后来转行学了数学。他说自己是在攻读博士学位期间对博弈论产生兴趣的，当时他在普林斯顿大学读书，参与了一项防御战略的制定和研究工作，项目假设一座城市被空袭，研究人员需要制定出一套防守战略，并就此展开研究。他在50年代从以色列移居美国。

谢林把研究工作扩大到冷战范畴之外。比如说，他的研究就表明，不同人群之间哪怕存在非常微小的差异，也有可能导致城内的大规模种族隔离行动。这套理论还将药物成瘾解释为针对自己的博弈。比如说，像戒烟的人可能会把香烟冲进马桶，因为他知道自己稍后可能无法抵御吸烟的诱惑。

诺贝尔经济学奖是唯一没有根据阿尔弗雷德?诺贝尔(Alfred Nobel)遗嘱颁发的奖项。这个奖项是在1968年创立的，被称为“瑞典银行为纪念阿尔弗雷德?诺贝尔而颁发的经济学奖”(Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel)。

Nobel prize for ‘game theory' thinkers


The Nobel prize for economics was awarded yesterday to Thomas Schelling and Robert Aumann for their individual contributions to the understanding of conflict and co-operation.

Both were pioneers in “game theory”, a branch of economics that now dominates the subject and is extremely important in other disciplines such as political theory, sociology and even biology. They will share the $1.3m (￡740,000, �1m) prize. Born in 1921, Mr Schelling, a professor at the University of Maryland, developed a theory of conflict situations that strongly influenced US attitudes towards nuclear deterrence in the cold war period of the 1950s and 1960s.

His 1960 book, The Strategy of Conflict, highlighted the importance of precommitment, brinkmanship and credible threats as strategic weapons in a tense stand-off between two parties. By limiting your own options, for example, you can make it clear to opponents how you will respond to their actions, whatever they do, thereby increasing the chances the other side will back down. Credible threats could also be made with brinkmanship, gradually increasing the probability of a conflict, Mr Schelling observed, adding that children understood brinkmanship perfectly.

Applied to the nuclear arms race, the theories gave the US its strategies to deal with the fundamental problem of how to get some use from weapons so terrible that their use could not really be contemplated.

Outside the geo-political sphere, Mr Schelling also found that people tended to co-operate more readily than a group of them behaving purely rationally would. Mr Aumann's contribution to strategic thinking around the subject of conflict and co-operation came in using logic and mathematics to understand the options available to people when they face the same opponents or competitors day-in, day-out.

When strategic situations are repeated very large numbers of times, even when individuals have immediate conflicts of interest, the opportunity for building co-operation increases because the individuals have to deal with the other side again and again in the future.

The analysis of “repeated games”, which Mr Aumann started, is now a mainstream part of all social sciences and applied to issues as diverse as political conflicts, irrigation systems, international treaties and collusion among companies.

Game theory was also the subject of the Nobel prize for economics sciences in 1994, when it was won by John Harsanyi, John Nash and Reinhard Selten. Paul Klemperer of Nuffield College, Oxford University, said the two economists came from different ends of the discipline, with Mr Schelling brilliantly intuitive and Mr Aumann one of the world's cleverest and most abstract economic thinkers. “It was an extremely natural choice,” he said. “The whole methodology [of game theory] has been so dominant in economics.”
诺奖授予博弈论先驱

诺贝尔经济学奖昨天授予了托马斯?谢林（Thomas Schelling）和罗伯特?奥曼（Robert Aumann），以表彰他们在促进对冲突与合作的理解方面所作的贡献。

他们两位都是“博弈论”（game theory）的先驱。作为经济学的一个分支，博弈论目前在该学科研究中占据主要地位，在政治理论、社会学甚至生物学等其他学科中也极为重要。两位获奖者将分享130万美元的奖金。生于1921年的谢林先生是马里兰大学教授，他曾提出了冲突局势理论，在上世纪50年代和60年代的冷战时期，该理论极大地影响了美国政府对核威慑的态度。

他于60年代出版的著作《冲突的战略》（The Strategy of Conflict），着力阐述了在双方处于僵持时，采取一些战略性手段的重要性。这些手段包括：事先承诺、边缘政策和有威慑力的威胁。例如，通过限定你自己的选择范围，你就可以使对手清楚地知道，你将对他们的行动作出何种反应――不管他们采取什么行动，这也就加大了他们作出让步的可能性。谢林先生发现，有威慑力的威胁也可以与边缘政策配合使用，以逐渐提高发生冲突的机率。他补充说，儿童对边缘政策的理解非常到位。


应用在核军备竞赛方面，上述理论为美国提供了处理一个根本问题的战略，这个问题就是如何发挥那些杀伤力极大武器的作用，由于它们的杀伤力太大，人们并不认为会真的投入使用。

在地缘政治领域之外，谢林先生还发现，人通常都是愿意合作的，但当他们在一个团队中完全依理性行事时，则不那么容易合作。奥曼先生对冲突与合作战略思想的贡献在于，他运用了逻辑学和数学来理解，当人们每天都面对相同对手或竞争者时，他们所能作出的选择。

当战略情形大量重复出现时，即便个体间有直接的利益冲突，达成合作的机率也会上升，因为每个个体在未来时间内，都会与另一方反复打交道。

奥曼率先提出的“重复博弈”分析，目前成为所有社会科学的主流分支，并已应用于政治冲突、灌溉系统、国际条约乃至公司相互勾结等各种各样的问题。

博弈论同时也是1994年诺贝尔经济学奖的获奖学科，该奖授予约翰?哈萨尼(John Harsanyi)、约翰?纳什(John Nash)及莱因哈德?泽尔腾(Reinhard Selten)。牛津大学纳菲尔德学院 (Nuffield College) 教授保罗?克伦佩雷尔(Paul Klemperer)表示，(此次获奖的)两位经济学家分别代表博弈论的不同观点。谢林有着极佳的直觉，而奥曼是经济学最为睿智和最善于抽象思维的学者。“这是再自然不过的选择，”他表示，“(博奕论的)整体方法论已在经济学领域占有极具支配力的地位。”