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纳什的诺贝尔奖(1994)

2017-04-25  cz6688


IT SOUNDS like a sports fan's dream. InStockholm on October 11th, three men shared a $1m prize for their skill atanalysing games. They are not television pundits, or armchair critics ofManchester United or the Miami Dolphins, but economists. Two Americans, JohnHarsanyi and John Nash, and a German, Reinhard Selten, have won this year'sNobel prize for economics for their studies of 'game theory'.


这听上去像是体育迷的梦想。1011日,在斯德哥尔摩,三人因为分析博弈的技能分享了100万美元的奖金。他们既不是电视评论员,也不是足不出户的曼联或者迈阿密海豚队的评论员,而是经济学家。两位美国人——约翰·海萨尼(John Harsanyi)和约翰·纳什(John Nash)——和一位德国人——赖因哈德·泽尔腾(Reinhard Selten)因为他们的“博弈论”研究赢得了今年的诺贝尔经济学奖。


Game theory may sound trivial. It is not.In the past 20 years or so it has revolutionised the economics of industrialorganisation and has influenced many other branches of the subject, notably thetheories of monetary policy and international trade. These days, no economicsstudents can hope to graduate without knowing the rudiments of it.


博弈论可能听起来无足轻重,实则不然。在过去的20多间,它彻底改变了产业组织经济学,影响了这门学科的许多其他分支,尤其是货币政策理论和国际贸易理论。如今,没有学经济的学生能够希望在不了解该理论基本常识的情况下毕业。


Odd though it may seem, until game theorycame along most economists assumed that firms could ignore the effects of theirbehaviour on the actions of others. That is fine when markets are perfectlycompetitive: what one firm or consumer does can make no difference to theoverall picture. Fine, too, when unchallenged monopolists hold sway: they haveno rivals to worry about.


尽管这可能似乎有点奇怪,但是,直到博弈论出现之前,大多数经济学家一直认为,企业是能够忽视它们的行为对他人行为的影响的。这在市场是完全完竞争时是对的:一家企业或一位消费者的所作所为的确影响不了大局。这在无人挑战的垄断者掌控大局时也是对的:它们没有要去担心的对手。


But in many instances this assumption iswrong. Many industries are dominated by a few firms: by building a new plant orcutting prices (or threatening to cut them), a firm can affect how its rivalsbehave. And it is not just in industrial economics that such calculationsmatter. Some countries may impose (or threaten) trade sanctions against othersin an attempt to prise open protected markets. A government may put upshort-term interest rates when inflation is low to convince financial marketsthat it is serious about fighting inflation; with luck, the markets will thenrequire lower long-term interest rates.


但是,在许多情况下,这种假设是错的。许多产业都是被少数几家企业所主宰:通过建造一家新工厂或是下调价格(亦或是威胁要下调价格)的方式,一家企业能够影响对手的具体行为。而且,这种明争暗斗不仅仅是在产业经济学中至关重要。有的国家可能为了打开受保护的市场对其他国家实施(或者是威胁实施)贸易制裁。政府可能会在通胀处于低位时推高短期利率,以便让市场相信它在打击通胀方面是认真的;顺利的话,随后,市场随将要求降低长期利率。


These examples are, in a way, just likegames: no football coach plans an attack without taking into account thedefenders' likely response. Modern game theory was fathered by John vonNeumann, a mathematician, and Oskar Morgenstern, an economist, who published 'Theoryof Games and Economic Behaviour' in 1944 (an anniversary which was notlost on this year's Nobel-prize givers). Messrs Harsanyi, Nash and Selten havehoned it into the sharp tool economists use today.


这些例子,从某种程度上来说,恰如体育比赛:没有足球教练会在不考虑防守一方的可能应对的情况下策划一次进攻。当代博弈论之父是数学家约翰·冯·诺伊曼John von Neumann)和在1944年出版了《博弈论和经济行为》(Theory of Games and Economic Behaviour)一书的和经济学家奥斯卡·摩根斯特恩。海萨尼、纳什和泽尔腾将其打造成了当今经济学家所使用的锋利工具。


In the early 1950s Mr Nash produced acompelling way of working out how games will end up when players cannot committhemselves, or do not want to collude with each other. A 'Nashequilibrium' occurs when no player wants to change his strategy, givenfull knowledge of other players' strategies.


 50年代初,纳什提出了一个令人信服的预测博弈在参与者不可能信守承诺或无意相互冲突的情况下将会如何结束的方式。“纳什均衡”发生在没有参与者想在已经完全知晓其他参与者策略的情况下改变策略之际。


Take one famous example of a Nashequilibrium. An industry has two firms (1 and 2). Each of them can choose a'high' or a 'low' price. If they both choose high prices,they make hefty profits, of $3m apiece. With low prices, they make only $2meach. But if one sets a high price and the other a low one, the low-price firmmakes $4m; the high-price firm gets a mere $1m. Although the firms would dobest if they both set high prices, they will not. If firm 1 sets a high prices,firm 2's best choice is to undercut it: it would earn $2m instead of $1m. Thesame goes for firm 1: it too sets a low price. So they both choose lowprices—and they make only $2m each.


以下就是纳什均衡的一个著名的例子。某产业有两家企业(12)。每一家企业都能选择“高的”或“低的”价格。如果都选择高的价格,各自获利300万美元。在低的价格下,各自只能获利200万美元。但是,如果一家企业设定是高的价格,另一家设定的是低的价格,那么,设定低价的那家企业获利400万美元,设定高价得到的只有区区100万美元。尽管这两家企业都会在双方都设定高的价格的情况下尽力而为,但是,它们是不会同时设定高的价格的。如果企业1设定的是高的价格,企业2的最佳选择是降低这个价格:它会盈利200万美元,而不是100万美元。对企业1来说也是如此:它也会设定一个低的价格。因此,两家企业全都设定低的价格。这样,只能各自获利200万美元。

 

But Mr Nash's work needed refining. First,it applies to games played only once, or in which players move simultaneously.But virtually all interesting economic games involve continual interactionbetween players. Mr Selten extended the Nash equilibrium to such settings. Fromthat emerges the importance of credibility: there is no point in one playerfollowing a plan which other players know will have to be changed at somepoint.


但是,纳什的研究需要进一步完善。首先,它适用于只进行一次或是参与者同步行动的博弈。但是,实际上,所有有趣的经济博弈全都涉及参与者之间的连续互动。泽尔腾将纳什均衡扩展到了这类情况。于是,出现了信誉的重要性:参与者按照别的参与者知道在某个时点必然会被改变的计划行事没有意义。


For example, a monopolist might try to keepa would-be rival out of its market by threatening a price war if the rivalsteps in. Such a war might mean that the entrant would make a loss. But itwould be costly for the monopolist, too. If the price war costs a lot, themonopolist would do better to share the market with the new entrant. In thatcase, the threat of a price war is not credible: the entrant can go into themarket, knowing that the incumbent would be foolish to fight back.


例如,垄断方可能会在对手介入时,试图通过威胁进行价格战的方式,将潜在的对手关在市场之外。这样一场战争可能意味着进入者会遭受损失。但是,这对垄断者来说,也会是非常昂贵的。如果价格战消耗巨大,垄断者就会宁愿与新的进入者分享市场。在这个例子中,价格战的威胁不是可信的:由于深知守成者会愚蠢到不发动反击,进入者是能够进入市场的。


Second, it is not realistic to assume thatthe players know what is in each other's minds. As Adam Brandenburger ofHarvard Business School puts it, 'games are played in a fog.' MrHarsanyi cut through the mist, by showing that games in which players are notwell informed about each other can be analysed in almost the same way asordinary games.


其次,假设参与者相互知根知底是不现实的。正如哈佛商学院的亚当·布兰登伯格(Adam Brandenburger)所言:“博弈是在迷雾中进行的。”海萨尼通过展示参与者之间不是很好地知根知底的博弈是能够用几乎与普通博弈相同的方式进行分析的办法揭开了这层迷雾。


When some players have information thatothers do not, their strategies can alter their reputations to their advantage.A government that shoves interest rates up to signal its anti-inflationarycredentials is one example. Or take a monopolist that would like to stop entryinto its market. It can do so if would-be rivals fear that it likes fightingprice wars, in spite of the cost. By fighting anyone who does enter, themonopolist can built a reputation as a price warrior and put other entrantsoff. And oligopolists may be able to keep profits up by setting high prices andnurturing reputations for being friendly to their rivals.


当某些参与者具有其他参与者所没有的信息时,他们的策略可能将它们的声誉变为优势。推高利率以昭示其反通胀信用的政府是一个例子。再比如希望阻止进入者进入其其市场的垄断者。它们可能会在潜在对手担心它们喜欢打价格战的情况下不计成本地做这种事。通过反击任何进入市场的人,垄断者能够树立起价格战勇士的名声,从而吓跑其他的进入者。而且,垄断者还可以通过设定高价和培育对对手友好的名声等方式保持利润上升。


Yet some economists are still wary of gametheory, despite the insights it has brought. That is partly because the theoryis difficult: it demands lots of tricky mathematics. That, however, is merely areflection of the complexity of the world. But there is a more tellingobjection—namely, that game theory is just that: theory. So far there have beenprecious few real-life applications. Game theorists have been good atexplaining the intricacies underlying strategic interdependence and producingever more refined concepts of equilibrium but less adept at giving governmentsand firms practical advice.


然而,有些经济学家仍然对博弈论持谨慎的态度,尽管它带来了众多的真知灼见。这部分是因为这个理论是有难度的:它要求许多棘手的数学知识。然而,这仅仅世界复杂性的一个反映。但是,还有一种更加显眼的反对意见——即,博弈论不过是理论而已。迄今为止,只有极少的真正实际应用。博弈论理论家虽然一直擅长解释构成战略依赖的复杂性并且始终在提出更加精炼的均衡概念,但却较不擅长于给政府和企业提出实用的建议。


Even that criticism, though, is weakening.Central bankers now know all about reputation and credibility. America'sFederal Communications Commission used game theorists to design this year'sauction of radio spectrum. And businesses, too, are beginning to learn aboutgame theory: Harvard's Mr Brandenburger, for example, teaches it to MBAstudents and executives. The time is coming, he says, when self-respectingMBAs, as well as economics graduates with a taste for maths, will not leaveschool without it.


然而,即便是这种批评也在日渐式微。如今,央行银行家知道有关名声和信誉的所有一切。美国联邦通信委员会使用了博弈论专家来设计今年的无线电频段拍卖。同时,商界也在开始研究博弈论:例如,哈佛商学院的布兰登伯格给MBA学生和高管教授博弈论。他说,除了对数学感兴趣的经济学毕业生之外,自尊自爱的MBA学生也不会在不学习博弈论的情况下离开学校的时代正在到来。

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