let us now revisit the solution concept 现在让我们重新审视解决方案概念
for extensive form games and let's start 进行广泛的形式游戏，让我们开始吧
by doing it let's start by looking at 通过这样做，让我们开始看
the following example in this game there 下面这个游戏中的例子
are a number of Nash equilibria and here 有一些纳什均衡，这里
is one of them BH see what is BH play 是其中之一BH看到BH玩什么
one goes down here and down here 一个人在这里和这里下来
whereas player two goes down here and 而第二个玩家在这里下来
down here under this strategy profile of 在此的战略概况下
course the outcome of the game is this 当然，游戏的结果是这样
one and the payoff to both players is 一个，两个玩家的收益是
five 五
let's first convince ourselves that this 首先让我们说服自己
is indeed a Nash equilibrium so let's 确实是纳什均衡，所以让我们
hold players one strategy fixed and see 固定玩家一项策略，看看
if player two can profitably deviate 如果玩家二可以有利地偏离
from their current response well what 从他们目前的反应来看
can they do they can say here I will 他们可以做到吗，我可以在这里说
instead of going C I would go D they 而不是去CI会去D他们
could say that but that would an impact 可以这么说，但这会产生影响
the outcome at all given that player two 给那个玩家两个，结果
is going down B and so that's not a 沿着B下降，所以这不是一个
profitable deviation wouldn't change 盈利偏差不会改变
their payoff the path to player two and 他们获得第二名玩家的收益，
the other thing they could do is say I'm 他们可以做的另一件事是说我
going to go down this this way but that 这样下去，但是那
would in fact worsen their payoff 实际上会恶化他们的收益
because they would end up here with a 因为他们最终会在这里
payoff of zero rather than the Pfizer 零回报而不是辉瑞
getting so player 2 cannot profitably 让玩家2无法获利
deviate from their current strategy what 偏离他们目前的策略是什么
apply what about player player one can 适用于玩家玩家可以做什么
they profitably deviate well what could 他们有利可图地偏离了什么
they do they could say okay rather than 他们会说可以，而不是说
go B I'll go a but then they will get a 去B我会去a但然后他们会得到a
payoff of three rather than the Pfizer 三分而不是辉瑞的回报
getting that not profitable and they 得到不赚钱，他们
could also say I'm going to go down G 还可以说我要去G
over here 在这里
but given that player 2 is going down e 但鉴于玩家2的失败率e
that wouldn't matter though in any case 无论如何都没关系
end up in this this outcome of the path 最终在这条路的这个结局中
of 5 and so that's not profitable 的5，所以没有利润
deviation either so neither player has a 要么偏差，要么没有球员有
profitable deviation then by definition 然后根据定义获利偏差
it's a Nash equilibrium but there's 这是纳什均衡，但有
something a little disturbing about this 对此有些困扰
equilibrium let's clear the slides it's 平衡让我们清除幻灯片
a little less messy and let's again 少一点混乱，让我们再次
write down the strategy for player 1 写下玩家1的策略
going be H and let's focus on Indy on 成为H，让我们专注于Indy
this node right there 这个节点就在那里
why would player 1 actually do H because 为什么玩家1实际上会做H，因为
G dominated the G they get a pair of 2 G统治了G他们得到了一对2
rather than 1 and so even though it did 而不是1，所以即使它确实
lead to a Nash equilibrium there's 导致纳什均衡
something a little troubling about it 有点困扰
and the way to understand it is by 而了解它的方法是
claiming that they would go down H here 声称他们会在这里H下
play 1 is threatening player 2 and 第一局威胁第二局玩家，
telling him listen do not consider going 告诉他听着不要考虑去
down here because I'm going to go down 在这里，因为我要下去
here therefore and you would get a zero 因此，在这里您将得到零
so you'd better go here and get a 5 is 所以你最好去这里得到5分
what player 1 saying is saying to player 玩家1对玩家说的是什么
2 but this is stretch is not credible 2，但是这是不可靠的
because after all player 2 said 因为毕竟玩家2说
player 1 says that but in fact it would 玩家1说，但实际上
not be in their interests I believe that 我相信不符合他们的利益
player 1 actually would go down here and 玩家1实际上会在这里下场
so how do we capture this in a formal 那么我们如何在正式形式中
definition that brings us to the notion 将我们带入概念的定义
of sub game perfect equilibria or sub 子游戏完美均衡或子
game perfection so let's first define 游戏完美，让我们先定义一下
the sub game it's a very obvious notion 子游戏是一个非常明显的概念
a looking at some node in the game node 看游戏节点中的某个节点
H the sub game of G rooted at H is a H植根于H的G的子游戏是
restricted restriction of H to this to H对此的限制
the descendants from from that from that 从那个的后代
node and similarly what are the set of 节点，类似的是什么
all sub games of G well look at all the G的所有子游戏都很好看
nodes in G G中的节点
the set of all sub games is simply all 所有子游戏的集合就是全部
the sub game routine at some node in G G中某个节点的子游戏例程
and so a national Librium is a sub game 因此，国家图书馆是一个子游戏
perfect if it's restriction to every sub 如果对每个子项都有限制，则完美
game is also a Nash equilibrium for that 博弈也是那什纳什均衡
that sub game so if for example we go to 该子游戏，例如，如果我们去
the previous slide and we consider again 上一张幻灯片，我们再次考虑
clearing the slide for a second and if 清除幻灯片一秒钟，如果
we look at the national erbium b h c e 我们看一下国家b
and we decide to Nash equilibrium but 然后我们决定达到纳什均衡
among the sub games of this game the 在这个游戏的子游戏中
subtrees of this tree of this tree is 这棵树的这棵树的子树是
this sub tree so here's a sub game it's 这个子树，所以这是一个子游戏
a game of a single player player 1 and 单人游戏1和
the restriction of this Nash equilibrium 纳什均衡的限制
is simply that's action of going H but 简直就是走H的动作，
this is not an equilibrium in this very 这不是一个平衡
simple tree because there's a profitable 简单的树，因为有一个有利可图的
deviation to G for the player and so 玩家的G偏差等等
while the to Nashville above the whole 而到纳什维尔最重要的是
tree is restriction to the sub tree here 树是对子树的限制
is not a Nash equilibrium 不是纳什均衡
and therefore this Nash equilibrium is 因此，纳什均衡是
not a sub game perfect and so so we see 不是完美的子游戏，所以我们看到了
that in fact that captures the intuition 实际上捕捉到了直觉
of non-credible threat and notice also 不可信任的威胁，并且还应注意
that one special case of the sub tree is 子树的一种特殊情况是
the entire tree so sub game perfect 整棵树，所以子游戏完美
equilibrium has got to also be a 平衡也必须是
national ribbon so let's test our 国家功能区，所以让我们测试一下
understanding of this concept a little 对这个概念有一点了解
bit let's look at this tree and ask 让我们看看这棵树，问一下
ourselves what are some of the sub game 我们自己是什么子游戏
perfect equilibria there for example how 那里有完美的平衡
about a g CF well the claim is this in 关于ag CF的说法是
fact is sub being perfect now why is 现在事实是完美的，为什么是
that what is a 那是什么
G C and F so that gives you this outcome GC和F，以便为您提供这种结果
over here and you can check there's no 在这里，你可以检查没有
profitable deviation but you can also 有利可图的偏差，但您也可以
ask in all the sub games is there 在所有子游戏中询问
profitable deviation well let's look at 有利可图的偏差让我们来看一下
some of the sub games well for example 例如一些子游戏
here there is a the stevie ation over 这里有一个方向
here but that would not be profitable 在这里，但那不会有利可图
for pair two because they would go down 对于第二对，因为他们会下去
from eight to three now but over here is 现在是八点到三点
their profitable deviation for example 例如他们的利润偏差
two player two not really because if 两个玩家两个不是真的，因为
they deviate it over here they would end 他们在这里偏离它会结束
up with a five random the ten they're 用五个随机数十个
getting how about over here is their 他们在这里过得如何
profitable deviation and this note to 有利可图的偏差和此注释
the agent one well no because if they 该代理人很好，因为他们
deviate they would get one rather than 偏离他们会得到一个而不是
two so in all sub games the restriction 在所有子游戏中有两个限制
of the strategy profile to that sub game 该子游戏的策略配置文件
is still a Nash equilibrium and a GCF is 仍然是纳什均衡，GCF是
in fact a sub game perfect Nash 实际上是一个完美的纳什子游戏
equilibrium how about bhce well the 平衡怎么样？
claim is that it's not well let's first 声称这不是很好，让我们先
write down the strategy bh b h and c e 写下策略bh bh和ce
and this is not sub game perfect for the 这不是子游戏的完美选择
reasons we saw before we saw that in 我们看到之前的原因
this sub game right here there is a 这个子游戏在这里有一个
profitable deviation for player one 玩家一的盈利偏差
namely to deviate over here and get to 即偏离这里并到达
rather than one and so it's not that 而不是一个，所以不是那个
being perfect and in fact for the same 是完美的，实际上是一样的
reason a HCF will not be sub game HCF不会成为子游戏的原因
perfect let's write down what a h CF is 完美，让我们写下什么是CF
a h CF you can check that it's a Nash 啊CF你可以检查一下那是纳什
equilibrium but it is a nut sub game 平衡，但这是一个疯狂的子博弈
perfect again this sub game here is 再次完美，这里的子游戏是
allows for profitable deviation on the 允许在
part of the player one so even though 即使是玩家的一部分
it's what's called off path even though 这就是所谓的偏路
player 1 makes sure that him that he 玩家1确保他
never gets to visit this node by going 永远不会去访问这个节点
down here even so it's not like perfect 即使在这里也不是很完美
because had he gotten here he would not 因为他到了这里他不会
have done what he claims he would have 已经完成了他声称的目标
done and that gives us a good sense for 完成，这使我们对
what is sub game perfect Nash 什么是子游戏完美纳什
equilibrium is 平衡是