博弈论 Game theory
1 英语原意
博弈论:Game theory
2 英文解释
Game Theory can help us find the ...
博弈论可以帮助我们找到…
- best decision in a competitive situation, or
在竞争形势下的最佳决策,或 - fairest decision in a cooperative situation
在合作的情况下最公平的决定
... where the outcome for each player depends on their decision and the decisions of other players.
...每个参与者的结果取决于他们的决定和其他参与者的决定。
It is useful in business, military, sports, finance, personal life, games and more.
它在商业、军事、体育、金融、个人生活、游戏等方面都很有用。
Let's have a look at an example to see how Game Theory can help us find the best decision.
让我们看一个例子,看看博弈论如何帮助我们找到最佳决策。
2.1 Prisoner's Dilemma 囚徒困境
Casey and Dana are arrested after a burglary. They are in separate rooms and cannot cooperate.
凯西和戴娜在一次入室盗窃后被捕。他们在不同的房间,无法合作。
Casey has been told:凯西被告知:
if you both stay quiet you both get 1 month in prison for trespass
如果你们都保持沉默,你们都将因非法侵入罪入狱一个月
if you accuse Dana: you go free, Dana gets 10 months
如果你指控Dana你就自由了,而Dana要被关10个月
if Dana accuses you: you get 10 months, Dana goes free
如果Dana指控你,你将被关10个月,而Dana就自由了
if you both blame each other you both get 6 months
如果你们互相指责,你们都被判6个月监禁。
What do you advise Casey to do? 你建议凯西怎么做?
... think about it for a bit ...
So maybe both Casey and Dana should keep quiet, right? They get only 1 month each that way..
所以也许凯西和戴娜都应该保持沉默,对吗?这样的话,他们每人只会被关一个月。
But that outcome is called 但这个结果被称为 unstable.不稳定
Because either side can do better by making the "I go free, you get 10 months" decision.
因为任何一方都可以做得更好,只需要指控对方,对方被关10个月,而自己就可以自由了。
So what to do?那该怎么办?
Well, sadly, Casey is better off blaming Dana.
很遗憾,凯西最好还是指控戴娜.
We can see it in a table like this:我们可以在这样的表格中看到:
Dana | |||
Stay Quie | Blame Casey | ||
Casey凯西 | Stay Quiet | -1, -1 | -10, 0 |
Blame Dana | 0, -10 | -6, -6 |
Casey risks getting 10 months by staying quiet! 凯西保持沉默可能会被判10个月!
So they will most likely get 6 months each.所以他们两个人很可能都会被关6个月。
2.3 Nash Equilibrium 纳什均衡
The set of player's strategies where Casey and Dana both blame each other (-6,-6) is a Nash Equilibrium, named after John Nash (the subject of the movie "A Beautiful Mind").
凯西和戴娜互相指控对方的策略集(-6,-6)是一个纳什均衡,以约翰·纳什(电影《美丽心灵》的主角)命名。
It is when no player is better off by changing only their own strategy.
当没有玩家可以只通过改变自己的策略而让全局变得更好的时,就会出现纳什均衡。
In the above example: at (-6,-6) Casey is not better off by changing to "quiet", and Dana is also not better off by changing to "quiet", so this is a Nash Equilibrium.
在上面的例子中:在(-6,-6)时,凯西并没有因为改变为“保持沉默”而变得更好,戴娜也没有因为改变为“保持沉默”而变得更好,所以这是一个纳什均衡。
(If they both changed to "quiet" they would both be better off, but we are only looking at individual choices here.)
(假如他们都改成了“保持沉默”,他们都会得到更好的结果,但我们在这里只看个人的选择。)
Another way of viewing it: if any player is better off changing then it is not a Nash Equilibrium.
换个角度来看,如果任何玩家改变策略会得到更好的结果,那么这就不是纳什均衡.
3 中文解释
博弈论主要研究公式化了的激励结构间的相互作用,是研究具有斗争或竞争性质现象的数学理论和方法。博弈论考虑游戏中的个体的预测行为和实际行为,并研究它们的优化策略。
博弈论是二人在平等的对局中各自利用对方的策略变换自己的对抗策略,达到取胜的目的。博弈论思想古已有之,中国古代的《孙子兵法》等著作就不仅是一部军事著作,而且算是最早的一部博弈论著作。博弈论最初主要研究象棋、桥牌、赌博中的胜负问题,人们对博弈局势的把握只停留在经验上,没有向理论化发展。
1994年诺贝尔经济学奖授予加利福尼亚大学伯克利分校的约翰·海萨尼(J.Harsanyi)、普林斯顿大学约翰·纳什(J.Nash)和德国波恩大学的赖因哈德·泽尔滕(Reinhard Selten),以表彰这三位数学家在非合作博弈的均衡分析理论方面做出了开创性的贡献,对博弈论和经济学产生了的重大影响。
4 感想体会
博弈论 Game theory,Game 不是游戏的意思吗?Game theory 就是如何赢得游戏的理论,为何翻译成博弈论?原本通俗易懂的英文单词,翻译成中文之后变得高深莫测。
参考文献:https://www.mathsisfun.com/sets/game-theory.html
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