A big pay-off for two game theorists
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.
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.
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.
Mutually assured co-operation
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.
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.
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.
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.