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Nash equilibrium 納什均衡

納什均衡，Nash equilibrium，又稱為非合作博弈均衡，是博弈論的一個重要術語，是納什發現的，以他的名字命名。它的含義是這樣的：假設有n個局中人參與博弈，給定其他人策略的條件下，每個局中人選擇自己的最優策略（個人最優策略可能依賴于也可能不依賴于他人的戰略），從而使自己效用最大化。所有局中人策略構成一個策略組合（Strategy Profile）。納什均衡指的是這樣一種戰略組合，這種策略組合由所有參與人最優策略組成。即在給定別人策略的情況下，沒有人有足夠理由打破這種均衡。

In game theory, the Nash equilibrium (named after John Forbes Nash, who proposed it) is a solution concept of a game involving two or more players, in which no player has anything to gain by changing only his or her own strategy unilaterally. If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium.

Stated simply, A and B are in Nash equilibrium if A is making the best decision A can, taking into account B's decision, and B is making the best decision B can, taking into account A's decision. Likewise, many players are in Nash equilibrium if each one is making the best decision that they can, taking into account the decisions of the others. However, Nash equilibrium does not necessarily mean the best cumulative payoff for all the players involved; in many cases all the players might improve their payoffs if they could somehow agree on strategies different from the Nash equilibrium (eg. competing businessmen forming a cartel in order to increase their profits). (answers.com)

影片中Nash以誰能得到金發美女這個博弈導出了自己的理論，算是導演對該理論的學以致用吧。

亞當?斯密 Adam Smith

亞當?斯密（Adam Smith，1723～1790），是英國古典政治經濟學的主要代表人物之一。他的代表作《國富論》（全稱《國民財富的性質和原因的研究》）被翻譯成十幾種文字，全球發行。而他本人也因此被奉為現代西方經濟學的鼻祖。《國富論》是一部劃時代的巨著。它概括了古典政治經濟學在形成階段的理論成就，最早系統地闡述了政治經濟學的各個主要學說，它標志著自由資本主義時代的到來。

Scottish philosopher Adam Smith is the author of the 1776 book An Inquiry into the Nature and Causes of the Wealth of Nations(《國富論》), a classic of modern economics beloved especially by free market advocates. He began his academic career as a professor of logic and moral philosophy in Glasgow (1751-64), but after about 1748 he was famously part of the Edinburgh intellectual circle that included David Hume. Smith gained international attention for his 1759 examination of societal ethics, Theory of Moral Sentiments, in which he argued that people are naturally empathetic to those suffering in their midst. But his Wealth of Nations secured Smith's fame -- the book sold out five editions during his lifetime, including revised versions in 1784 and 1789. He is credited with being the first to examine the importance of the division of labor and worker productivity, and for advancing the idea that free markets thrive on the basis of mutual self-interest. Although Smith warned against monopolies and mercantilism, his notion that markets are driven toward the public good by an "invisible hand" has made him a venerated figure among free market doctrinaires. He spent his last years in Edinburgh as a government official, as the Commissioner of Customs.

Most sources list his birthdate as 5 June 1723, the date of his baptism. His father died before Smith was born; Smith lived with his mother most of his life and never married. (Who2biography)

考考你

將下面的句子譯成英語。

1. 大家總是擔心誰會控制原油市場。

2. 說到下象棋，我的女婿一般都能贏。

3. 影片的一些部分以慢動作重放。

4. 我作為朋友前去和他面談，但遭到了他的拒絕。

A beautiful mind《美麗心靈》精講之一考考你參考答案

1. 我同意我們應當以改進效率為目標。

I agree that we should set our sights on improving efficiency.

2. 以我之見，戒煙對你來說是明智的。

In my opinion, you'd be wise to rid yourself of the smoking habit.

3. 他沒有耐心。

Patience is not his strong suit.

影片對白 Adam Smith needs revision.

(英語點津Annabel編輯)

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