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永远不会结束的博弈 – 译学馆
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永远不会结束的博弈

The Game That Never Ends

Vsauce, Kevin here,
这里是《维瑟科普》 我是凯文
with a slot car race track to visualize how fast I can safely drive
今天我要用轨道赛车向大家展示 在不被开罚单的情况下
without getting pulled over.
我可以把车开到多快
What’s my maximum speed without wreaking havoc on the justice system?
也就是说 在不挑战法律体系的前提下 我能达到的最高时速是多少
And how can we use game theory to find the answer?
以及如何用博弈论来找到答案
Here we go.
一起来看看吧
Oop.
哎呀
Oop.
哎呀
Alright, that didn’t really work out very well.
好吧 似乎效果不太理想
Honestly, I don’t even have enough room
说实话 我甚至都没有足够的空间
to properly set up this track on this table.
在桌子上摆放好轨道
So, um,
所以 呃
I’m gonna need some help.
我需要一些帮助
Luckily, I partnered with CuriosityStream, and I know just the guy.
幸运的是 我和CuriosityStream有合作 并且刚好认识一个可以帮到我的人
Hey, Sean.
嘿 肖恩
As host of the awesome new CuriosityStream show, Speed,
CuriosityStream旗下的新节目Speed十分精彩 你作为主持人
I was hoping that you could help me visualize speeding,
我希望你能帮我展示一下超速
but it looks like you already have
但看起来你似乎已经
– Yeah, well. – The track here.
– 没错 – 铺好了轨道
Kevin, to do just that,
凯文 为了帮到你
I have magically manifested exactly the same track that you have,
我已经神奇地复制了和你一模一样的赛车轨道
right here on my table.
就在这张桌子上
– Super convenient. – Yeah.
– 实在太方便了 – 是的
Boom. Okay, so…
嘣 那么
Let’s race.
我们开始赛车吧
I will be the cop car, and you will be the civilian driver.
我来控制警车 你来控制民用车
I wouldn’t have it any other way.
我别无选择
Okay, do I get a head start?
好 那我先开始吗
Yes.
是的
I’m gonna pull you over.
我肯定完胜你
Let’s go.
开始
Well, let’s go.
好 开始
– Uh huh. Okay, so I’m racing ahead. – Yeah.
– 嗯 好的 现在我领先一步了 – 没错
There’s a turbo button,
这里有一个加速按钮
which you can use kind of in the straight way.
你可以在直线跑道上使用它
– That’s helping me gain on you, actually. – Yeah.
– 实际上它在帮我追上你 – 没错
– But, – Oh.
– 但是 – 噢
If you turbo in the corner, it’s too much speed and you’ll fly right off.
如果你在转弯处加速 车速将会过快 你的车会直接飞出跑道
Why did that happen, though?
那么为什么会发生这种事呢?
Okay, that happens because, in this case,
发生这种事的原因是 这种情况下
you exceeded the coefficient of friction between the tires, and the slot, and the top of the track.
你超出了轮胎 凹槽以及轨道之间的摩擦系数
These cars, they can go around the corner a lot faster than a normal car can,
这种小赛车比正常车过弯道要快得多
because they have this little peg that’s riding in that slot.
因为它们装有这个能够嵌在凹槽轨道里的小桩
Yeah.
是的
So when they go around the corner,
所以当小赛车过弯时
they’re resisting centripetal force
它们在对抗
which wants to sling it off the one the car wants to keep going in the straight line.
将小车拉离直行轨道的向心力
Right.
没错
But this slot helps drag it around the corner.
但这个凹槽会把它拽回弯道
Now in our cars, we don’t have a slot.
现实中 我们的车并不是嵌在这样的凹槽中行驶
So if we go around a corner too fast,
所以如果我们过弯太快
we slide off when we exceed the coefficient of friction of our tires.
我们的车就会因为超过轮胎的摩擦系数而飞出去
And our tires, though they look kind of big,
而车子的轮胎尽管看起来很大
they really don’t have that much space on the road.
但它们和路面的接触面积其实并没有很大
I’m gonna show you that.
我来给你展示一下
I brought one of the tires off one of my motorbikes here.
我从我的一辆摩托车上取下了一个轮胎
I’m just gonna Sharpie the top here
我先在这上面用马克笔做个标记
and this looks like a pretty big round tire, right?
这个轮胎看起来又大又圆 对吧
Rides down the road.
准备上路了
Only when it’s riding down the road on the street,
只有当它在路上跑的时候
it’s really only got about one inch.
接触面其实只有大约一英寸宽
Wow.

Right, if we take a look at that there,
是的 让我们来看看
there’s really only about one inch wide and maybe three inches long.
纸上的印记其实只有大概一英寸宽和三英寸长
That’s the contact between me, and the motorcycle, and the ground.
这是我和摩托车轮胎与地面之间的接触面
The same is true on the tires on your car, right?
你车上的轮胎也是一样的道理 对吗
The tire’s all the way round
轮胎总是圆的
but the only part that’s actually touching the ground
但是实际上接触地面的部分
is that little bit on the bottom.
只有底部的那一小部分
And if you have your tires overinflated,
而且如果你给轮胎充气太满
you are getting a much smaller contact patch.
接触面甚至会更小
That makes sense.
有道理
Tire’s not deforming.
轮胎就不易变形了
Yeah, yeah.
是的
So that little bit, the contact patch, is important to understand.
所以理解那一小块接触面是很关键的
You got four these little contact patches.
你的车一共有四个这样的小接触面
They are maybe four inches by five inches wide on your four tires.
它们一共有大概四英寸x五英寸大小 分布在你的四个轮胎上
And the weight of that car pushing down on that contact patch
车子施加在这个接触面上的重量
is the only thing that keeps you from sliding off the road when you go around a corner.
是唯一能防止你的车在过弯时偏离道路的力
The weight of the car, the inertia of the car, wants it to keep going straight.
车子的重量和惯性会让它保持直行
When you turn the car, the front wheels move off in one direction,
当你转向时 车子的前轮会偏向一边
and the friction makes those tires track around the corner.
摩擦力会帮助轮胎过弯
The reason that’s important
这一点很重要
is because you are also using that same friction,
是因为你不仅在过弯时会用到这个摩擦力
not only to go around the corner, but you are using it to accelerate and to brake.
你在加速和刹车的时候也同样会用到
If you accelerate too fast,
如果你加速太快
you overcome the coefficient of friction between your tires and the ground
由于刚才提到的接触面非常小 你会超过轮胎和地面之间的摩擦系数
with that little contact patch, and you do a burnout.
从而产生翻车的危险
Mm hmm.

It can actually be a lot of fun in a controlled environment.
在可控的环境中 这其实可以很有趣
But the more important thing for all of us driving around,
但是对于我们所有驾车的人而言
that’s really really pertinent to our safety is that
更重要的 也是与我们的安全息息相关的事情就是
the faster you go,
你开的越快
you are asking more and more of that little tiny contact patch
你就会越依赖那一小块接触面
to help slow you down when you hit the brakes.
来帮助你在刹车时减速
So if you are going way faster,
所以如果你开的越快
you have to be easier on the brakes.
你就越需要轻踩刹车
If you lock up the brakes,
如果你把刹车踩死
you’ll slide the whole car forward, and that’s what’s happening here.
那么整个车身就会向前打滑 就像刚才发生的那样
It’s just you are carrying too much speed into the turn,
你的车刚才以过快的速度进入弯道
tires and the slot can’t take it, and you are sliding right off the track.
轮胎和凹槽之间的摩擦力不足以限制住小赛车 导致它脱轨飞了出去
Wanna try it again?
还想再试一次吗
Yeah, yeah. Um, where’s the cop car?
好呀 呃 不过警车飞到哪里去了
Let’s restore the…
让我们把小赛车重新归位
Go ahead.
来吧
Okay. Here we go.
好 开始了
So that’s a technical reason why you don’t wanna speed,
所以这是你不想超速的一个技术原因
but there’s a lot of other reasons why you don’t wanna speed too, right?
但同时还有很多其他的原因使你不想超速 对吗
Yeah. I mean, that’s why it’s dangerous to speed,
是的 我是说 刚才我们探讨的是超速的危险性
but also in society, you know, we have to have…
而在现实生活中 你懂的 我们必须要有
Oop. There we go.
哎呀 又飞出去了
In society, we can’t have that happening.
现实生活中 我们不能让这种事发生的
No, we can’t have that happening.
是的 我们不能让这种事发生
You know, we want everyone to be safe.
你知道的 我们希望每个人都安全
And we have rules and regulations, and law enforcement in place
我们有各种各样的规章制度和执法机构
to make sure that everyone is acting safely.
来确保每个人都能安全驾驶
The thing we don’t really think about is that
我们却没有考虑到
driving in a system governed by law enforcement is actually a two-player game.
在交通执法体系的约束下驾驶汽车 实际上可以理解为双人博弈
And both the driver and the police officer are playing this game.
司机和交警便是这场博弈的局中人
Let’s say that the speed limit is 65 miles per hour.
我们假设一段路的限速为时速65英里
What’s the fastest that you’ve ever driven?
你曾经最快开到多少
Cuz I have a feeling it’s a lot more than that.
因为我猜一定比时速65英里要快得多
I’ve driven about 130 miles an hour.
我曾经开到过时速130英里
Okay, but my question is,
好吧 但我有个问题
what is a sensible speed to drive on the highway?
在高速上开到多少速度比较合理呢
The answer to that question is somewhat complicated,
这个问题的答案有点复杂
cuz it really depends on the highway, and the conditions,
因为这取决于路况 行车条件
and if it’s raining, and the state of your car, right?
是否下雨 以及你的车况 对吗
But in general, for roads that are,
但总的来说
we collectively deem we need to go slower in,
对于有些道路我们会达成共识 认为应该降低车速
because either it’s near neighbourhood,
因为它们邻近社区
or because the road itself is twistier,
或者路本身很崎岖
we have lower speed limits.
那么这些路段的最高限速就会低一些
And then we have big straight super highways
同时我们有宽阔而笔直的高速公路
where we can all do 75
在那里我们就可以开到时速75英里
or whatever the limit is in your area.
或者你们当地规定的较高限速
But the point is that
但是问题在于
cops can’t pull over every single driver
交警不可能把每一辆
just for going one mile per hour over whatever that limit is
仅仅超过限速一英里每小时的车都拦下来
because not only is that logistically impossible,
因为这不仅是不现实的
but that level of law enforcement would probably make everyone pretty angry.
而且这种执法力度很可能让所有人都觉得愤怒
So when we drive and the police monitor us,
所以当我们驾车的时候 交警在监督我们
we are playing a game of recursion to get the best result.
我们是在进行一种寻求最佳结果的递归博弈
Both of the police and the drivers are sort of playing this game from different sides.
交警和司机是从不同的角度进行博弈
Exactly, exactly.
没错 完全正确
We’ve got a couple of basic rules in this game.
在这局博弈中我们有一些基本规则
We have a legal speed limit of,
我们有法定限速
let’s say 65 miles per hour.
假设限速是时速65英里
And we have common sense rules that tell us that we can only go so fast
同时常识告诉我们不能开得太快
before it gets dangerous and we are flying off the edge of the road
否则就会有飞出路边的危险
And the police officer has a threshold at which he or she will ticket the driver.
交警也会有一个底线 如果司机触及这个底线 就会收到罚单
So each player is deciding what to do based on
所以每个局中人所选择的行动都是基于
what they think the other player will do.
他们所认为的另一个局中人会做出的行动
Yeah, there’s a gray area, isn’t there?
是的 有灰色地带 对吧
Yeah. It basically works like this.
是的 大致上是如下这样
As the cop,
作为交警
I’m thinking how fast does Sean think that he can go without getting pulled over.
我会揣摩肖恩认为他在不被交警拦下的情况下能开多快
Right. And as the driver, I’m thinking,
是的 作为司机 我会揣摩
how fast can I get away with,
开到多快我还能逃过法眼
without getting pulled over.
不被交警拦下
Exactly, exactly.
是的 完全正确
And as the cop, I’m also thinking
作为交警 我还会揣摩
how fast does Sean think I think he thinks he can go,
肖恩自己揣摩到的我所认为的他能开到的最快速度是多少
when he’s thinking, how fast do I think he thinks he can go.
同时他也在揣摩 我所揣摩到的他能开到的最快速度是多少
And that’s recursion.
这就是所谓的递归
At the end of this process, which can be infinite,
在这个过程最后 当然它可能无限循环
both the driver and the cop decide their best courses of action.
司机和交警都会确定他们最佳的行动方案
For the driver, that’s like you said,
对于司机而言 就像你刚才说的
how fast he can go safely without getting a ticket.
他能以多快的安全驾驶速度避开罚单
And for the cop,
对交警而言
that’s how fast he’ll let the driver go before pulling him over.
他允许司机开到多快而不会将他们拦下
Right, and this whole game takes place in that gray area.
是的 而且整个博弈发生在刚才提到的灰色地带
I mean I know if I stay under 65,
我是说 我知道如果我的时速保持在65英里以下
I’ll never get pulled over.
我就一定不会被交警拦下
That’s the easy way to do it, right?
这是相对比较容易的方法 对吧
And I know if I go 130, I’m gonna get pulled over.
同时我知道如果我的时速达到130英里 我就会被交警拦下
So there’s this strip there,
所以这里包含了一个速度区间
and that’s the gray area where that game you’re talking about is getting played.
这就是你刚才探讨的博弈所在的灰色地带
Ultimately, so what do you think would be an exact value
那么经过所有这些分析之后 如果限速是时速65英里
if the limit was 65 miles per hour that we could get.
你认为我们可以开到的最快时速的确切值是多少
Like you could drive without getting pulled over,
也就是说 可以让你不被交警拦下
and so that you are happy with the speed that you are going.
并且你自己对这个速度也很满意
I think it’s general wisdom that you can get away with
我认为一种普遍观点是
about five miles over the speed limit,
最多可以超过限速约五英里每小时
especially on the highway
尤其是在高速公路上时
when there is no chance of coming across a stop sign or someone on the road, right?
几乎不可能遇到停车标志或行人 对吧
So when there’s…
所以如果
in a safe environment like that I think everybody pretty much feels like
在这样一种相对安全的环境下 人们普遍认为
they can go five miles over the speed limit and not get pulled over,
可以超过限速五英里每小时而不会被交警拦下
or somewhere in that gray area.
或者在这个灰色地带以内的其他速度
Both the police and the speeder
交警和超速的司机
are playing this game from their own sides, right?
从不同的角度参与这局博弈 对吗
The speeder’s trying to figure out how fast they can get away with.
超速司机想要弄清能够避免罚单的最快速度
The police’s trying to figure out how much they’ll allow.
而交警想要弄清他们应该允许超速多少
But they both have an incentive to make the whole system work.
但他们双方都有动机让这个体系有效运转
So when they both play the game
所以当他们在进行博弈时
and they find this place where they get to speed a little
他们找到了可以稍微超速
and don’t get pulled over there
但又不会被开罚单的情况
In that gray area, they find a balance.
在灰色地带中他们找到了一种平衡
And that balance is called a Nash Equilibrium.
这种平衡叫做纳什均衡
What Sean described is the best reply to another player’s best action.
肖恩所描述的是博弈的一方对另一方的最优行动 所作出的最优反应
And when neither player has an incentive to deviate from their decision,
当双方都没有动机去偏离他们的决策时
they’ve reached a Nash Equilibrium.
他们就达到了纳什均衡
Okay, I need to talk more about Nash Equilibrium,
好的 关于纳什均衡我还需要再讲一些
but I need my whiteboard table.
但我需要用到我的白板桌子
So thank you so much, Sean, for all of your help.
所以在此非常感谢肖恩的帮助
Make sure you watch his show, Speed, on CuriosityStream.
观众朋友们一定要看他在CuriosityStream上主持的Speed
I know that you guys will love it.
我保证你们一定会喜欢的
But for now,
但现在
I have to, I have to, I have to go.
我真的真的真的该走了
Okay, now one of the most famous Nash Equilibrium scenarios
好的 那么用来理解纳什均衡的最著名的情境
comes in the form of the well-known Prisoner’s Dilemma.
莫过于大家耳熟能详的囚徒困境
The scene is simple. Two people get arrested for a crime.
情境很简单 两个人因犯罪而被捕入狱
They’re separated and can’t communicate with each other.
他们被隔离 不能互相交流
The police can convict both on a lesser charge,
警察可以直接给他们两个定小罪
but they need more proof to convict them on the big one.
但是却需要更多的证据来定更大的罪
That means one has to testify that the other did the crime.
这就意味着其中一个罪犯必须要指认另一个有罪
So is it in each prisoner’s best interest
所以这两个囚徒从自身利益的角度出发
to rat on the other one or to stay quiet?
他们是应该选择出卖对方还是保持沉默呢
Here’s how it plays out.
让我们来看看具体分析
If both prisoners A and B rat on each other,
如果囚徒A和B互相出卖对方
they’ll each get two years in prison.
他们两个都会在监狱服刑两年
If A blames B, but B stays quiet,
如果A出卖B 但是B保持沉默
A goes free and B gets three years in prison, and vice versa.
A就会被释放 而B需要在监狱服刑三年 反过来也是一样
If both A and B stay quiet,
如果A和B都保持沉默
they’ll each get one year in prison.
他们两个就会在监狱服刑一年
The rational prisoner rats,
一个理性的的囚徒会选择出卖对方
because that’s the only way he’s going to go free.
因为那是唯一可以让他被释放的方法
And when he rats, it always gives him a better result than if he doesn’t rat
当他出卖对方时 不管另一个囚徒做出什么选择
regardless of what the other prisoner does.
他自己都会得到比保持沉默更好的结果
That’s called a dominant strategy.
这就叫做优势策略
And the Nash Equilibrium in the Prisoner’s Dilemma
囚徒困境中的纳什均衡
is achieved by betrayal.
通过囚徒间的互相背叛来实现
But if the other prisoner also behaves rationally,
但是如果另一个囚徒也是理性的
he would rat as well,
那么他也会选择出卖对方
and they’d both get two years.
那么两个囚徒就都需要在监狱服刑两年
The best course of action here is cooperation,
在这里最优的行动方案其实是双方合作
where both stay quiet, serve a lesser sentence,
也就是两个囚徒都保持沉默 使得服刑时间更短
and have the least bad outcome.
以取得最少的坏结果
In the Prisoner’s Dilemma,
在囚徒困境中
not betraying the other guy goes against the Nash Equilibrium,
不背叛另一个人的行为是不符合纳什均衡的
but it gives the best possible result for both players combined.
但如果把两个局中人当成一个整体来考虑 这会产生最好的结果
Because if one rats and the other doesn’t,
因为如果一个囚徒选择出卖而另一个没有
three years are served.
两人的服刑总时间为三年
And if they both rat, four years are served.
如果双方都选择出卖 那么总的服刑时间就是四年
Through cooperation, only two years are served.
而如果两人合作 保持沉默 那么总的服刑时间只有两年
Political scientist Robert Axelrod asked 14 game theory experts
政治学家罗伯特·阿克塞尔罗德曾让14个博弈论专家
to submit computer simulations of the Prisoner’s Dilemma.
提供电脑模拟的囚徒困境的数据结果
The ones that advocated more self-interest by betrayal
那些提倡通过背叛来获得更多个人利益的人
were noted as “not nice” players,
被称为“不友善”局中人
while the ones that focused on cooperation, they were “nice”.
而那些注重合作的人 被称为“友善”局中人
After running them all,
在完成全部模拟后
the top half of the performers were all “nice” models,
取得更好结果的一半都是“友善”局中人
while the bottom half were all “not nice”.
而另一半结果相对不好的都是“不友善”局中人
So it pays to be nice
所以友善会有回报
as long as the other player thinks it pays to be nice, too.
当然前提是对方也认为友善会有回报
We play these two-player games all day long, not just with the police.
我们每天都在进行双人博弈 不仅仅是和交警
When we give a gift, we’re playing a game.
当我们在送礼物时 其实也是在进行博弈
For example, say you’ve just met someone,
举个例子 你刚认识一个人
and you kinda like them.
你有一点喜欢这个人
Giving them a spatula is probably not a great gift.
送对方一个小铲子可能不算很好的礼物
Giving them a diamond ring on the second date is probably a bit much.
而在第二次约会时就送对方钻戒 可能又有些太过火
Pump the brakes there.
你不能让荷尔蒙冲昏了头脑
Billy.
说你呢 比利
In the gift-giving game,
在送礼博弈中
you want to send the right message based on what you feel,
你想根据内心真实感受送出正确的礼物
and the recursive process that happens with what you think they’ll feel.
在你揣摩别人收到礼物的感受时 递归过程就会发生
You want to feel good about the gift you gave
你想对自己送出的礼物满意
and they want to feel good about the gift they’ve received.
而对方想要对自己收到的礼物感到满意
And whether you’re driving down the highway or trying to impress your crush,
无论你是在高速公路上行驶 还是想给你的心动对象留下好印象
you’re almost always in some kind of two-player game,
你都是在进行双人博弈
and sometimes you’re in several at once.
而且有时候你同时身处于多局双人博弈中
The best way to play is to be smart,
不管怎样 博弈的最佳策略一定是学聪明
to pay attention,
专注点
and keep your best interest in mind.
时刻牢记自己的切身利益所在
But you’ll usually win the most
但你要想赢的最多
when you make sure to be nice.
那你要确保友善待人
I guess grandma was right.
看来 奶奶的教诲是对的
And as always, thanks for watching.
还是老规矩 谢谢收看
Hey. Gigantic thanks to Sean Riley for opening up his shop to me.
嘿 十分感谢肖恩·莱利为我提供的帮助
Go check out his brand new show Speed.
去看看他主持的最新节目Speed
It’s a four-part docuseries
这是个四部分组成的纪录片
where Sean blasts through humanity’s need for speed.
肖恩以一种激动人心的方式来展示人类对速度的激情
On land. Wow.
不管是在陆地上 哇
On sea, through the skies, and into space.
还是在海里 天空上 太空中
CuriosityStream and I worked out a deal for you
CuriosityStream和我共同为粉丝提供了福利
so that can sign up and get 30 days completely free.
注册即可得到30天免费试用
Just click the link below and go to CuriosityStream.com/Vsauce2
只需点击下方链接进入网站
and enter the promo code vsauce2,
并且输入邀请码vsauce2
all lowercase.
全部小写
CuriosityStream gives you unlimited access to over 2,400 brain-feeding documentaries
CuriosityStream为你准备了超过2400部充实头脑的纪录片
starting at just $2.99 per month.
每月只需2.99美元
But for you,
但是 对你而言
you can watch Sean’s show free by using the promo code vsauce2.
你可以通过使用vsauce2邀请码免费观看肖恩的节目
So you should do that.
所以你应该去看
The show is awesome.
这个节目非常棒
Honestly.
说真的
You’ll like it.
你会喜欢的
Go watch it.
去看看吧
Go watch it now.
现在就去看看吧
Okay.
好吧
Now.
马上行动起来

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视频概述

这是一个用有趣易懂的例子解释纳什均衡的科普视频,通过现场演示和理论讲解完成,值得一看。

听录译者

收集自网络

翻译译者

JZ

审核员

审核员AL

视频来源

https://www.youtube.com/watch?v=kI712FeoPSM

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