let us now look at some examples and of 现在让我们来看一些例子
games and Nash equilibria in those games 游戏和那些游戏中的纳什均衡
so here's the first game a familiar game 所以这是第一个熟悉的游戏
this is of course the prisoner's dilemma 这当然是囚犯的困境
the if both prisoners cooperate and 如果两个囚犯合作，
content and then they get a light 内容，然后他们就亮了
punishment and if they do not cooperate 惩罚，如果他们不配合
they get a more severe punishment if the 他们会受到更严厉的惩罚
one cooperates and the others does not 一个合作而其他不合作
then the co-op irrigated terrible 然后合作社灌溉很糟糕
punishment and the one that does not 惩罚与不惩罚
cooperate gets off scot it gets off 合作下车苏格兰人下车
scot-free and of course this game has a 无苏格兰人，当然这个游戏有
dominant strategy to defect no matter 主导缺陷策略无论如何
what the other agent does you're better 另一个代理商你做得更好
off not cooperating and so of course the 不合作，所以当然
only dominant strategy outcome is this 唯一的主要策略结果是
one of both defecting and indeed that is 既有缺陷，又有缺陷的是
the only Nash equilibrium in this game 这场比赛中唯一的纳什均衡
so it's the Nash equilibrium it's the 所以这是纳什均衡
best response if the other person 如果对方最佳反应
defects then it's the best respond to 缺陷，那么它是最好的应对方法
defect but in fact it's much stronger 缺陷，但实际上要强大得多
than that it's best to defect no matter 最好不要有任何缺点
what the other the other agent does so 另一个代理人这样做
this is an example of one unique Nash 这是一个独特的纳什的例子
equilibrium that happened to be very 恰好是非常均衡
strong one a dominant strategy Nash 强势策略Nash
equilibrium so so here's another game 平衡，所以这是另一个游戏
this is the game of pure coordination I 这是纯粹协调的游戏
think of it as walking towards each 认为它是走向每个
other on the sidewalk and you both can 其他人行道上，你们俩都可以
decide whether to go to your respective 决定是否去你各自的
lifts or respective rights in both cases 两种情况下的升降机或各自的权利
you will do fine and you will not 你会做得很好，你不会
collide and of course if you miss 碰撞，当然，如果您想念
coordinate if you one goes to the left 协调，如果你去左边
and the other to the right you will 另一个在右边
collide so this is a natural game and in 碰撞，所以这是自然的游戏
fact you see that you have two Nash 事实上你看到你有两个纳什
equilibria the one that I wrote down 平衡我写下的那一个
here if one one of the players goes to 如果一位玩家去
the left it's the best respond to go to 左边是最好的回应
the left and conversely if the other 左边，反之亦然
player goes to the right you're best off 玩家向右走，你最好
going to the right as well and the 也会向右走，
others are not Nash equilibria so here's 其他人不是纳什均衡，所以这里的
an exam 考试
of a game where there are two Nash 一个游戏中有两个纳什
equilibria or to specifically pure 均衡或特纯
strategy Nash equilibria again we'll 策略纳什均衡再一次
discuss why we call these pure strategy 讨论为什么我们称这些为纯策略
later on here's a very different game 稍后这是一个非常不同的游戏
this is often called the game of battle 这通常被称为战斗游戏
of the sexes imagine a couple and they 的性别想象一对夫妇，他们
want to go together to a movie and 想一起去看电影，
they're considering two movies one of 他们正在考虑两部电影之一
them a very violent movie Battle of the 他们是一部非常暴力的电影
Titans and the other very relaxed movie 泰坦和另一部非常轻松的电影
about flower growing called Lee's B&F 关于花的成长，叫做李的B＆F
the wife of course would prefer to go to 妻子当然更愿意去
battle of the Titans and the the husband 泰坦与丈夫之战
would prefer to watch flower growing but 宁愿看花开，但
more than anything else they would want 比他们想要的更重要
to go together and so here are the 一起去，所以这里是
payoffs if they both go to battle of the 如果他们都参加战斗的话
Titans then they're both positively 泰坦然后他们都是积极的
happy their wife more than the husband 妻子比丈夫更快乐
if the go both go to the flower growing 如果两者都去花开
movie then the husband is slightly happy 电影，然后丈夫有点高兴
and the wife but if they go to different 和妻子，但如果他们去不同的地方
movies neither of them is happy that's 电影他们俩都不开心
that's that's the that's that's the the 那就是那那就是那
game how many how many equilibria we 游戏我们多少平衡
have here well again we have two pure 再来一遍，我们有两个纯
strategy Nash equilibria why is that 策略纳什均衡为什么
well if either them goes to the Battle 好吧，如果他们去参加战斗
of the Titans then the other one would 的泰坦，然后另一个
want to go there too because if they go 也想去那里，因为如果他们去
to a different one they would get zero 换成另一种，他们将得到零
rather than whatever they get here one 而不是他们来到这里
or two depending on whether the husband 一两个取决于丈夫
of the wife and conversely on the on the 的妻子，相反在
flower watching movie flower grow movie 花看电影花种电影
and so in both cases they were the best 所以在两种情况下它们都是最好的
response is to go to the movie selected 回应是去看电影
by the other party so on the face of it 对方如此面对
it looks very similar to the game of 它看起来非常类似于
pure coordination that we have here but 我们在这里有纯粹的协调，但是
we do see a slight difference here and 我们在这里确实看到了细微的差别，
it will revisit that later on when we 稍后，当我们
speak about not pure strategies but 谈论的不是纯粹的策略，而是
mixed strategies 混合策略
here's a here's another example the last 这是一个这是另一个例子
one we'll look at and this is the game 我们来看一看，这就是游戏
called matching pennies imagine each of 所谓的匹配便士想象每个
us two players needing to just need to 我们两个玩家只需要
decide on some side of a of a coin heads 在硬币头的a的某一侧决定
or tail if we decide on the same size 还是尾巴，如果我们决定相同的尺寸
heads or tail but we decide on the same 头或尾，但我们决定相同
one then then I win if we decide on 一个然后我赢了，如果我们决定
different sides you heads and me tails 你的头和我的尾巴的不同侧面
or vice versa the new win and so we see 反之亦然，新的胜利，所以我们看到
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
we both decides on tails I win and 我们都决定我赢的尾巴，
otherwise you win by winning I mean I 不然你赢了就是我
get 1 you get minus 1 so this is a 得到1你得到负1所以这是一个
zero-sum game the sum of our payoff is 0 零和游戏，我们的收益之和为0
what is a pure strategy Nash equilibrium 什么是纯策略纳什均衡
here let's think about it suppose I pick 让我们考虑一下，假设我选择了
head what is your best response well 领导什么是你最好的反应
your best response then is to pick tails 你最好的选择就是挑尾巴
because you get one rather than minus 因为你得到一个而不是减
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
response is not to play tail because I 回应不是打尾巴，因为我
want to coordinate with you because then 想和你协调，因为
I will get one rather than minus one 我会得到一个而不是减一
that I would be getting here but now if 我会到这里，但现在如果
I play tails you'd rather play heads 我打尾巴你宁可打头
because you'd get one rather than the 因为你会得到一个而不是
minus one you're getting here but again 减一，你要来这里，但是再来一次
if you're playing tails I want to if you 如果你在打尾巴，我想
playing heads I want to play heads to 我要打头
match so we have this cycle where the 匹配，所以我们有这个周期
best responses are leading us in the 最好的回应正在引领我们
cycle and so there is no pure strategy 周期，所以没有纯粹的策略
Nash equilibrium in this game of mashing 这场捣蛋游戏中的纳什均衡
pennies 便士