Game theory: Prison breakthrough

Game theory: Prison breakthrough
The fifth of our series on seminal economic ideas looks at the Nash equilibrium.
JOHN NASH arrived at Princeton University in 1948 to start his PhD with a one-sentence recommendation: “He is a mathematical genius”
.
He did not disappoint.

Aged 19 and with just one undergraduate economics course to his name, in his first 14 months as a graduate he produced the work that would end up, in 1994, winning him a Nobel prize in economics for his contribution to game theory.
On November 16th 1949, Nash sent a note barely longer than a page to the Proceedings of the National Academy of Sciences, in which he laid out the concept that has since become known as the “Nash equilibrium”.
This concept describes a stable outcome that results from people or institutions making rational choices based on what they think others will do.
In a Nash equilibrium, no one is able to improve their own situation by changing strategy: each person is doing as well as they possibly can, even if that does not mean the optimal outcome for society.
With a flourish of elegant mathematics, Nash showed that every “game” with a finite number of players, each with a finite number of options to choose from, would have at least one such equilibrium.
His insights expanded the scope of economics.
In perfectly competitive markets, where there are no barriers to entry and everyone’s products are identical, no individual buyer or seller can influence the market: none need pay close attention to what the others are up to.
But most markets are not like this: the decisions of rivals and customers matter.
From auctions to labour markets, the Nash equilibrium gave the dismal science a way to make real-world predictions based on information about each person’s incentives.
One example in particular has come to symbolise the equilibrium: the prisoner’s dilemma.
Nash used algebra and numbers to set out this situation in an expanded paper published in 1951, but the version familiar to economics students is altogether more gripping.
(Nash’s thesis adviser, Albert Tucker, came up with it for a talk he gave to a group of psychologists. )
It involves two mobsters sweating in separate prison cells, each contemplating the same deal offered by the district attorney.
If they both confess to a bloody murder, they each face ten years in jail.
If one stays quiet while the other snitches, then the snitch will get a reward, while the other will face a lifetime in jail.
And if both hold their tongue, then they each face a minor charge, and only a year in the clink.
There is only one Nash-equilibrium solution to the prisoner’s dilemma: both confess.
Each is a best response to the other’s strategy; since the other might have spilled the beans, snitching avoids a lifetime in jail.
The tragedy is that if only they could work out some way of co-ordinating, they could both make themselves better off.
The example illustrates that crowds can be foolish as well as wise; what is best for the individual can be disastrous for the group.
This tragic outcome is all too common in the real world.
Left freely to plunder the sea, individuals will fish more than is best for the group, depleting fish stocks.
Employees competing to impress their boss by staying longest in the office will encourage workforce exhaustion.
Banks have an incentive to lend more rather than sit things out when house prices shoot up.
The Nash equilibrium helped economists to understand how self-improving individuals could lead to self-harming crowds.
Better still, it helped them to tackle the problem: they just had to make sure that every individual faced the best incentives possible.
If things still went wrong—parents failing to vaccinate their children against measles, say—then it must be because people were not acting in their own self-interest.
In such cases, the public-policy challenge would be one of information.
Nash’s idea had antecedents.
In 1838 August Cournot, a French economist, theorised that in a market with only two competing companies, each would see the disadvantages of pursuing market share by boosting output, in the form of lower prices and thinner profit margins.
Unwittingly, Cournot had stumbled across an example of a Nash equilibrium.
It made sense for each firm to set production levels based on the strategy of its competitor; consumers, however, would end up with less stuff and higher prices than if full-blooded competition had prevailed.
Another pioneer was John von Neumann, a Hungarian mathematician.
In 1928, the year Nash was born, von Neumann outlined a first formal theory of games, showing that in two-person, zero-sum games, there would always be an equilibrium.
When Nash shared his finding with von Neumann, by then an intellectual demigod, the latter dismissed the result as “trivial”, seeing it as little more than an extension of his own, earlier proof.
In fact, von Neumann’s focus on two-person, zero-sum games left only a very narrow set of applications for his theory.
Most of these settings were military in nature.
One such was the idea of mutually assured destruction, in which equilibrium is reached by arming adversaries with nuclear weapons (some have suggested that the film character of Dr Strangelove was based on von Neumann) .
None of this was particularly useful for thinking about situations—including most types of market—in which one party’s victory does not automatically imply the other’s defeat.
Even so, the economics profession initially shared von Neumann’s assessment, and largely overlooked Nash’s discovery.
He threw himself into other mathematical pursuits, but his huge promise was undermined when in 1959 he started suffering from delusions and paranoia.
His wife had him hospitalised; upon his release, he became a familiar figure around the Princeton campus, talking to himself and scribbling on blackboards.

重点单词
extension [iks’tenʃən] n. 伸展，延长，扩充，电话分机
assessment [ə’sesmənt] n. 估价，评估
declaration [.deklə’reiʃən] n. 宣布，宣言
stable [‘steibl] adj. 稳定的，安定的，可靠的 n. 马厩，
challenge [‘tʃælindʒ] n. 挑战 v. 向 … 挑战
impress [im’pres] n. 印象，特徵，印记 v. 使 … 有印
canal [kə’næl] n. 运河，沟渠，气管，食管 vt. 建运河，
dismal [‘dizməl] adj. 阴沉的，凄凉的，暗的
destruction [di’strʌkʃən] n. 破坏，毁灭，破坏者
defeat [di’fi:t] n. 败北，挫败
翻译
六大经济思想之五——纳什均衡。
1948年，约翰·纳什带着一句话的推荐信——他是一个数学天才——来到普林斯顿大学开始读博。
他没有令人失望。
年仅19岁且名下只有一个经济学课程的他，在读博的头14月中就交出了最终会在1994年因为对博弈论的贡献而为他赢得了诺贝尔经济学奖的研究。
1949年11月16日，纳什给《美国国家科学院院刊》寄去了一份刚够一页纸长的笔记，在这份笔记中，他提出了自此闻名遐迩的“纳什均衡”概念。
这个概念描述了一种源自个人或机构基于自身之于别人将做什么的认识而做出理性选择的稳定结果。
在纳什均衡中，无人能够通过改变策略而改善自身境况：每一个人都在尽其所能地做事，虽然这不意味着社会的最佳结果。
借助于优雅数学的表述，纳什告诉人们：每一场参与者数量有限每一位参与者可供选择的选项数量也是有限的“博弈”都至少会有一个这样的均衡。
他的高见扩展了经济学的范围。
在完全竞争市场中，没有进入门槛且所有人的产品都完全相同，没有单独的买方或卖方能够影响市场：谁也不需要密切关注别人正在忙什么。
但是，大多数市场不是如此：对手和客户的决定至关重要。
从拍卖到劳动力市场，纳什均衡给这门沉闷科学提供了一种基于每一个人的动机信息做出现实生活预测的方法。
一个例子尤其代表了这种均衡：囚徒困境。
纳什曾在1951年发表的一篇延伸论文中运用代数和数字论述了这种情景。但是，经济学学生熟悉的版本更为吸引人。
(纳什的论文导师阿尔伯特·塔克尔曾在对一群心理学家的谈话中提到过它。)
它说的是两名正在单独牢房中如坐针毡的犯罪分子，每个人都在考虑由地区检察官提出的同样交易。
如果他们双双承认身犯命案，每人都面临十年牢狱。
如果一个人坚持不说，另一个人告密揭发，告密之人将得到奖赏，而另外那个人将面临终身监禁；
如果两人都闭口不言，那么，每个人都面临较小的指控，而且只有一年刑期。
对这种囚徒困境，只存在一种纳什均衡的解决方案：两人双双坦白。
每一方的坦白都是对对方策略的最佳应对；因为另一个人可能说漏嘴，告密揭发避免了终身监禁。
悲剧就在于，如果他们能够找到合作之法，两人都可能让自己的处境好起来。
这个例子表明，除了明智之外，众人也可能是愚蠢的；个体的最佳可能是集体的灾难。
在现实世界中，这种悲剧性结果太常见了。
耗尽渔业资源的涸泽而渔，利在个人，弊在集体；
通过最长时间地待在办公室中的办法而博得老板印象的雇员将鼓励员工耗尽精力；
房价大涨的时候，银行有动力放出更多贷款，而不是袖手旁观。
纳什均衡曾给经济学家理解自我完善的个人如何能够成为自暴伤害的大众提供了帮助。
更重要的是，它还曾帮助他们去解决这个问题：他们只需确认，每一个单独的个人都面对最佳激励可能。
如果仍然出现问题——例如父母没能让孩子接种麻疹疫苗——那么，这必然是因为当时人们没有以符合自身利益的方式行事。
在这种情况下，公共政策的挑战会是信息的挑战。
纳什的思想有先例。
1838年，法国经济学家奥古斯丁·古诺提出了下面这种理论：在只有两家竞争公司的市场中，每一家公司都会看到通过提高产出，以更低的价格和更微薄的利润形式，来追求市场份额的弊端。
有意无意之间，古诺发现了一个纳什均衡的例子。
对于每一家来说，根据竞争对手的策略决定生产水平是有意义的；然而，在激烈竞争占上风的前提下，消费者最终面对越来越少的商品和越来越高的价格。
另一位先驱是匈牙利数学家约翰·冯·诺依曼。
1928年，即纳什出生的那一年，冯·诺依曼概述了最早的正式博弈论，表明，在两人的零和博弈中，向来存在一种均衡。
当纳什把自己的发现与当时已是知识分子偶像的冯·诺依曼分享时，后者斥之为 “无关紧要” 的结果，认为它不过是他自己早期证明的一种延伸而已。
实际上，冯·诺依曼之于两人零和博弈的强调只给他的理论留下了非常狭窄的应用。
这些前提大都是军事性的。
其中之一就是其中的均衡是由于装备了核武器的的对手才达到的相互确保毁灭的思想。(有人认为，奇爱博士这位电影人物就是以冯·诺依曼为原型的) .
在这些前提中，没有一种对考虑一方的胜利并非自动地意味着另一方的失败的情形——包括大多数类型的市场——特别有用。
即便如此，经济学界一开始还是认可了冯·诺依曼的评估，并在很大程度上忽视了纳什的发现。
纳什一头扎进了自己在数学方面的其他追求，但是，当他在1959年开始遭受幻觉和强迫症折磨时他的远大前程遭遇了灭顶之灾。
他的妻子把他送进了医院；出院后，他成了普林斯顿校园中的一个熟悉的身影，不是自言自语，就是在黑板上涂涂写写。

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