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let us now look at some examples and of
现在让我们来看一些例子

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games and Nash equilibria in those games
游戏和那些游戏中的纳什均衡

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so here's the first game a familiar game
所以这是第一个熟悉的游戏

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this is of course the prisoner's dilemma
这当然是囚犯的困境

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the if both prisoners cooperate and
如果两个囚犯合作， 

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content and then they get a light
内容，然后他们就亮了

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punishment and if they do not cooperate
惩罚，如果他们不配合

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they get a more severe punishment if the
他们会受到更严厉的惩罚

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one cooperates and the others does not
一个合作而其他不合作

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then the co-op irrigated terrible
然后合作社灌溉很糟糕

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punishment and the one that does not
惩罚与不惩罚

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cooperate gets off scot it gets off
合作下车苏格兰人下车

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scot-free and of course this game has a
无苏格兰人，当然这个游戏有

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dominant strategy to defect no matter
主导缺陷策略无论如何

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what the other agent does you're better
另一个代理商你做得更好

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off not cooperating and so of course the
不合作，所以当然

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only dominant strategy outcome is this
唯一的主要策略结果是

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one of both defecting and indeed that is
既有缺陷，又有缺陷的是

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the only Nash equilibrium in this game
这场比赛中唯一的纳什均衡

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so it's the Nash equilibrium it's the
所以这是纳什均衡

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best response if the other person
如果对方最佳反应

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defects then it's the best respond to
缺陷，那么它是最好的应对方法

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defect but in fact it's much stronger
缺陷，但实际上要强大得多

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than that it's best to defect no matter
最好不要有任何缺点

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what the other the other agent does so
另一个代理人这样做

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this is an example of one unique Nash
这是一个独特的纳什的例子

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equilibrium that happened to be very
恰好是非常均衡

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strong one a dominant strategy Nash
强势策略Nash 

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equilibrium so so here's another game
平衡，所以这是另一个游戏

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this is the game of pure coordination I
这是纯粹协调的游戏

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think of it as walking towards each
认为它是走向每个

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other on the sidewalk and you both can
其他人行道上，你们俩都可以

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decide whether to go to your respective
决定是否去你各自的

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lifts or respective rights in both cases
两种情况下的升降机或各自的权利

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you will do fine and you will not
你会做得很好，你不会

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collide and of course if you miss
碰撞，当然，如果您想念

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coordinate if you one goes to the left
协调，如果你去左边

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and the other to the right you will
另一个在右边

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collide so this is a natural game and in
碰撞，所以这是自然的游戏

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fact you see that you have two Nash
事实上你看到你有两个纳什

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equilibria the one that I wrote down
平衡我写下的那一个

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here if one one of the players goes to
如果一位玩家去

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the left it's the best respond to go to
左边是最好的回应

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the left and conversely if the other
左边，反之亦然

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player goes to the right you're best off
玩家向右走，你最好

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going to the right as well and the
也会向右走， 

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others are not Nash equilibria so here's
其他人不是纳什均衡，所以这里的

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an exam
考试

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of a game where there are two Nash
一个游戏中有两个纳什

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equilibria or to specifically pure
均衡或特纯

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strategy Nash equilibria again we'll
策略纳什均衡再一次

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discuss why we call these pure strategy
讨论为什么我们称这些为纯策略

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later on here's a very different game
稍后这是一个非常不同的游戏

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this is often called the game of battle
这通常被称为战斗游戏

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of the sexes imagine a couple and they
的性别想象一对夫妇，他们

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want to go together to a movie and
想一起去看电影， 

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they're considering two movies one of
他们正在考虑两部电影之一

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them a very violent movie Battle of the
他们是一部非常暴力的电影

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Titans and the other very relaxed movie
泰坦和另一部非常轻松的电影

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about flower growing called Lee's B&F
关于花的成长，叫做李的B＆F 

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the wife of course would prefer to go to
妻子当然更愿意去

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battle of the Titans and the the husband
泰坦与丈夫之战

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would prefer to watch flower growing but
宁愿看花开，但

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more than anything else they would want
比他们想要的更重要

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to go together and so here are the
一起去，所以这里是

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payoffs if they both go to battle of the
如果他们都参加战斗的话

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Titans then they're both positively
泰坦然后他们都是积极的

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happy their wife more than the husband
妻子比丈夫更快乐

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if the go both go to the flower growing
如果两者都去花开

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movie then the husband is slightly happy
电影，然后丈夫有点高兴

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and the wife but if they go to different
和妻子，但如果他们去不同的地方

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movies neither of them is happy that's
电影他们俩都不开心

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that's that's the that's that's the the
那就是那那就是那

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game how many how many equilibria we
游戏我们多少平衡

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have here well again we have two pure
再来一遍，我们有两个纯

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strategy Nash equilibria why is that
策略纳什均衡为什么

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well if either them goes to the Battle
好吧，如果他们去参加战斗

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of the Titans then the other one would
的泰坦，然后另一个

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want to go there too because if they go
也想去那里，因为如果他们去

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to a different one they would get zero
换成另一种，他们将得到零

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rather than whatever they get here one
而不是他们来到这里

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or two depending on whether the husband
一两个取决于丈夫

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of the wife and conversely on the on the
的妻子，相反在

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flower watching movie flower grow movie
花看电影花种电影

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and so in both cases they were the best
所以在两种情况下它们都是最好的

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response is to go to the movie selected
回应是去看电影

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by the other party so on the face of it
对方如此面对

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it looks very similar to the game of
它看起来非常类似于

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pure coordination that we have here but
我们在这里有纯粹的协调，但是

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we do see a slight difference here and
我们在这里确实看到了细微的差别， 

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it will revisit that later on when we
稍后，当我们

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speak about not pure strategies but
谈论的不是纯粹的策略，而是

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mixed strategies
混合策略

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here's a here's another example the last
这是一个这是另一个例子

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one we'll look at and this is the game
我们来看一看，这就是游戏

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called matching pennies imagine each of
所谓的匹配便士想象每个

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us two players needing to just need to
我们两个玩家只需要

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decide on some side of a of a coin heads
在硬币头的a的某一侧决定

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or tail if we decide on the same size
还是尾巴，如果我们决定相同的尺寸

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heads or tail but we decide on the same
头或尾，但我们决定相同

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one then then I win if we decide on
一个然后我赢了，如果我们决定

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different sides you heads and me tails
你的头和我的尾巴的不同侧面

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or vice versa the new win and so we see
反之亦然，新的胜利，所以我们看到

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this here if we both decides on heads or
如果我们俩都决定要这样做，还是在这里

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we both decides on tails I win and
我们都决定我赢的尾巴， 

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otherwise you win by winning I mean I
不然你赢了就是我

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get 1 you get minus 1 so this is a
得到1你得到负1所以这是一个

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zero-sum game the sum of our payoff is 0
零和游戏，我们的收益之和为0 

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what is a pure strategy Nash equilibrium
什么是纯策略纳什均衡

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here let's think about it suppose I pick
让我们考虑一下，假设我选择了

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head what is your best response well
领导什么是你最好的反应

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your best response then is to pick tails
你最好的选择就是挑尾巴

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because you get one rather than minus
因为你得到一个而不是减

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one but if you pick I tails then my best
一个，但是如果你选择我尾巴，那我最好

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response is not to play tail because I
回应不是打尾巴，因为我

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want to coordinate with you because then
想和你协调，因为

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I will get one rather than minus one
我会得到一个而不是减一

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that I would be getting here but now if
我会到这里，但现在如果

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I play tails you'd rather play heads
我打尾巴你宁可打头

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because you'd get one rather than the
因为你会得到一个而不是

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minus one you're getting here but again
减一，你要来这里，但是再来一次

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if you're playing tails I want to if you
如果你在打尾巴，我想

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playing heads I want to play heads to
我要打头

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match so we have this cycle where the
匹配，所以我们有这个周期

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best responses are leading us in the
最好的回应正在引领我们

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cycle and so there is no pure strategy
周期，所以没有纯粹的策略

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Nash equilibrium in this game of mashing
这场捣蛋游戏中的纳什均衡

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pennies
便士