in this video I'm going to tell you 在这个视频中，我要告诉你
about how to define formally the 关于如何正式定义
imperfect information extensive form and 不完善的信息广泛形式和
how to reason about strategies in these 如何推理这些策略
games so in the perfect information 游戏中的完美信息
extensive form we have a player take an 广泛的形式，我们有一个球员采取
action at every single choice node in 在每个选择节点上的动作
the game and a consequence of that 游戏及其后果
definition is that we're saying that 定义是我们在说
players know what node they're in all 玩家知道他们在哪个节点
the time and that means they know the 时间，这意味着他们知道
whole history of all of the moves that 所有动作的整个历史
have happened before in the game this is 在游戏中发生过，这是
reasonable for some games like chess 对于象棋这样的游戏来说是合理的
where you really do get to see what your 你真正在哪里看到你的
opponent does in every different move 对手的动作各不相同
it's not reasonable for games like 对于像这样的游戏是不合理的
battleship where your play your opponent 您扮演对手的战舰
can do something and you don't get to 可以做某事而你却无法
see what it is and it matters to to what 看看它是什么，对什么都重要
happens to you later in the game it can 在游戏的后面发生在你身上
matter to your payoff it can matter to 对您的回报至关重要，对
whether the game stops or continues so 游戏是停止还是继续
in order to model this richer situation 为了模拟这种更丰富的情况
where players aren't able to observe 玩家无法观察的地方
everything that their opponents do we're 他们对手所做的一切
going to add something new to the game - 将为游戏添加一些新内容-
the game representation so we're going 游戏表示，所以我们要去
to call it the imperfect information 称其为不完善的信息
extensive form and the way this is going 广泛的形式以及前进的方向
to work is we're going to take the old 上班是我们要把旧的
definition that we had before but we're 我们以前有过的定义
going to say that players consider some 会说玩家考虑一些
choice nodes to be equivalent to each 选择节点等效于每个
other so there's some choice nodes that 其他的还有一些选择节点
a player I isn't able to tell apart and 我无法分辨的球员
that's going to mean they're not able to 这将意味着他们无法
completely figure out the history of 完全弄清楚历史
where they are in the tree because 他们在树上的位置是因为
they're not going to know which of 他们不会知道哪个
several choice nodes they're out when 几个选择节点
they have to take a choice and we're 他们必须做出选择，我们
going to do this by taking the set of 通过采取一组来做到这一点
choice nodes for a given player and 给定玩家的选择节点，以及
putting them into equivalence classes so 将它们放在等价类中
what that means is kind of schematically 这意味着是示意性的
if these are some different choice nodes 如果这些是一些不同的选择节点
in the game that all of course belong to 在游戏中，所有当然都属于
the same player we might say these are 我们可能会说这些球员是
one equivalence class these are another 一个等价类，这是另一个
equivalence class and these are a third 等值课程，这是第三
equivalence class and what that would 等效类以及那会是什么
mean is the player wouldn't know which 意思是玩家不会知道哪个
of these two choice nodes 这两个选择节点中的一个
I he was at when he was asked to make a 当他被要求制作一个
choice but he would know that he was at 选择，但他会知道他在
one of these two and not one of these 这两个之一，而不是其中之一
two because they're in different 两个，因为他们是不同的
equivalence classes so let's say that a 等价类，所以说
little bit more formally 正式一点
so to formally define an imperfect 从而正式定义一个不完美
information extensive form game we start 我们开始的信息丰富的形式游戏
with a perfect information extensive 拥有完善的信息
form game which we've already learned 我们已经学过的形式游戏
how to define before and then we're 如何定义之前，然后我们
going to add this ingredient of 要添加这个成分
equivalence classes so we're going to 等价类，所以我们将
add this element I which is a set of 添加这个元素我是一组
equivalent set of sets of equivalence 等价的等价集
classes one for every player so for 为每个玩家分配一个，因此
player one we have the set of 玩家一，我们有一套
equivalence classes or let's say for 等价类，或者说
player I we have a set of equivalence 玩家，我有一组等效
classes numbered from 1 to K sub I so 从1到K子类的编号
these are all different equivalence 这些都是等价的
classes and each one of these classes is 类，这些类中的每一个是
some number of different choice notes 一些不同的选择笔记
one or more choice notes and these are 一个或多个选择说明，这些是
going to be different choice nodes that 将成为不同的选择节点
that player isn't able to tell apart so 该玩家无法分辨，所以
if every one of these equivalence 如果这些等价的每一个
classes contains only one choice node 类仅包含一个选择节点
we're back with the perfect information 我们回来了，完美的信息
case and if any of these equivalence 情况，以及是否有这些等同物
classes contains more than one thing 类包含不止一件事
then we have something new we have a 然后我们有了新的东西
game where the player doesn't quite know 玩家不太了解的游戏
what's going on all the time now in 现在一直在发生什么
order to make this definition work we 为了使这个定义可行，我们
need to add a couple of restrictions so 需要添加一些限制，所以
that it makes sense so we want to say 这很有意义，所以我们想说
that if and if two different choice 如果，如果两个不同的选择
nodes are part of the same equivalence 节点是同等的一部分
class then first of all they have to 上课，那么他们首先要
belong to the same player they have to 属于他们必须同一个球员
be labeled with the same player because 被标记为同一个玩家，因为
if they're not you'd be able to tell 如果不是，您将能够告诉他们
them apart because they different 他们分开是因为他们不同
players would be acting so the player 玩家会表演，所以玩家
kind of when he shows up he would know 当他出现时，他会知道
which player he was he would really not 他是哪个球员，他真的不会
be confused about all of the nodes in 对中的所有节点感到困惑
the equivalence class and the second 等价类和第二类
restriction we have is that the two 我们有两个限制
choice nodes have to have the same set 选择节点必须具有相同的集合
of available actions because if the 可用操作，因为如果
player can't tell them apart he has to 玩家无法将他们分开，他必须
know what to do and it's the only 知道该怎么办，这是唯一的
restrictions so let's look at an example 限制，让我们来看一个例子
game here and see what the equivalence 在这里比赛，看看等效
classes are so in this game player one 在这个玩家中上课是这样的
has two different equivalence classes 有两个不同的等价类
this is one equivalence class and this 这是一个等价类
is another equivalence class so in other 是另一个等价类，所以在其他
words we're going to use a dotted line 我们将使用虚线的单词
here to connect together choice nodes 这里将选择节点连接在一起
that belong to 属于
the same equivalence class and what we 相同的等价类以及我们
want to say in this game is that player 想在这场比赛中说的是那个球员
1 moves and if he goes right then the 1移动，如果他走对，则
game is just going to end and they're 游戏即将结束，他们
just going to get a each of half of one 只会得到一半的一半
if he goes left then they're going to 如果他走了，那他们将
get to make player two is going to get 成为第二个玩家
to make a choice and player 2 is going 做出选择，而玩家2将会
to go either A or B and then player 1 is 去A或B然后玩家1是
going to get to move a second time but 打算再去一次，但是
player 1 isn't going to get to observe 玩家1不会观察
the move that player 2 took and so he's 玩家2采取的行动，所以他是
going to have to take the same action 将不得不采取相同的行动
regardless of whether he said this 不管他是否这么说
choice noted this choice node and indeed 选择记录了这个选择节点，实际上
you can see we've labeled it the same 您可以看到我们已将其标记为相同
way so if he says he wants to go left he 这样，如果他说他想离开他
would have to go left it from both of 将不得不从两个
these notes and just to complete the 这些笔记，只是为了完成
answer to my question what are the 回答我的问题是什么
equivalence classes for player 2 玩家2的等效课程
well player 2 only has one choice node 玩家2只有一个选择节点
actually there's a typo here there 其实这里有错字
shouldn't be a 2 player 2 has only one 不应该是2位玩家2位只有一位
choice node and so he has only one 选择节点，所以他只有一个
equivalence class so how should we 等值课程，那么我们应该如何
define the pure strategies for each 为每个定义纯策略
player in this game what's going to make 这个游戏的玩家将要做什么
sense as a definition of pure strategies 感觉是纯粹策略的定义
well intuitively remember before what we 直观地记得我们之前
said was that we had the cross-product 说是我们有交叉产品
of all of the different action sets for 的所有不同操作集中
each player we don't want that here 我们不想在这里的每个球员
because we don't want for it to be 因为我们不希望它成为
possible for player 1 to do something 玩家1可以做某事
different in this choice node and in 在这个选择节点和
this choice node so instead what we're 这个选择节点，所以我们是
going to use as a definition is that the 用作定义是
pure strategies for player I are the 我是玩家的纯策略
cross-product of the action sets in 动作的叉积
every different equivalence class that 每个不同的等价类
he has and so player one's pure 他有，所以玩家是纯粹的
strategies here are going to be a choice 这里的策略将是一个选择
here and independently a choice here so 在这里，这里是一个独立的选择
player one could take the action LL or 玩家可以采取行动LL或
he could take the action RL or you could 他可以采取行动RL，也可以
take the action L R or RR so player one 采取LR或RR的动作，让玩家一
here has four different pure strategies 这里有四种不同的纯策略
rather than eight as he would have if we 而不是他的八倍
didn't have this equivalence class here 这里没有这个等效课程
so in the imperfect information normal 所以在不完美的信息中正常
form we have a more powerful 形式我们有一个更强大的
representation than we did in the 代表性比我们在
perfect information case and one way we 完美的信息案例和我们的一种方式
can see that is we can represent any 可以看到那是我们可以代表任何
normal form game in this representation 此表示形式的普通形式游戏
which you may recall we couldn't do with 您可能还记得我们无法做到的
perfect information games so here I'm 完美的信息游戏，所以我在这里
showing you how to represent the TCP 向您展示如何表示TCP
back-off game or in other words the 退避游戏或换句话说
prisoner's dilemma game in imperfect 不完美的囚徒困境游戏
information extensive form so how does 信息扩展形式，如何
this work well first of all player 1 首先玩家1运作良好
gets to decide whether to cooperate or 决定是否合作或
defect and after that player 2 gets to 缺陷，然后玩家2进入
decide whether to cooperate a defect now 现在决定是否合作缺陷
of course in the prisoner's dilemma you 当然在囚徒困境中
don't get to see what the other person 不要去看对方
chose to do when you take your own 选择自己去做时
action so it might sound like a problem 行动，所以听起来好像是个问题
that player 2 gets to move second but 玩家2获得第二
player 2 isn't able to tell which action 玩家2无法判断哪个动作
player 1 took and so although our game 玩家1参加了比赛，尽管我们的比赛
representation says that he goes second 表示说他屈居第二
it doesn't really make a difference that 它并没有真正改变
he goes second because because he's not 他获得第二名是因为他没有
informed of what player 1 did and then 告知玩家1的行为，然后
once both of them take their actions we 他们俩一旦采取行动，我们
end up with some payoff so if they go C 最终得到一些回报，所以如果他们去C
D and they end up with this payoff here D，他们最终在这里得到了回报
and these are the same payoffs that we 这些是与我们相同的收益
have in the game matrix notice that we 在游戏矩阵中注意到我们
could have things work the same way if 可以让事情以相同的方式运作，如果
we put player 2 at the root node and 我们将播放器2放在根节点上，
player 1 down here below because time 玩家1在这里的下方，因为时间
isn't really playing a role in this game 在这个游戏中并没有真正扮演角色
so I what I told you on the previous 所以我以前告诉过你的
slide was how to start with a normal 幻灯片是如何从正常开始
form game and make an extensive form 形式游戏并进行广泛的形式
game out of it I can also still do the 游戏出来，我仍然可以
thing that we talked about with the 我们谈论的东西
perfect information extensive form which 完善的信息广泛形式
is to start with an extensive form game 从一个广泛的形式游戏开始
and make a normal form game out of it 然后用它制作一个普通的形式游戏
and the way this works is exactly the 而它的工作方式正是
way I did before so I take all of the 我以前做的方式，所以我把所有
pure strategies for player 1 and I make 我和玩家1的纯策略
them into rows I take all of the pure 他们成排，我把所有的纯
strategies for player 2 and I make them 玩家2的策略，我让他们
into columns and then this gives me my 列，然后这给了我我的
matrix and for every cell of the matrix 矩阵以及矩阵的每个单元格
I say well if player 1 took this pure 我说好，如果玩家1接受了
strategy and player 2 took this pure 策略和玩家2采取了这种纯
strategy what payoff would result and I 策略会带来什么回报，我
put that into this cell of the matrix 把它放到矩阵的这个单元格中
and I fill in the whole matrix that way 然后我以这种方式填写整个矩阵
and once I have the matrix like that 一旦我有了这样的矩阵
then then I'm kind of done my definition 然后我就完成了定义
of mixed strategies is exactly what it 混合策略正是它的目的
was before it's just the mixed 之前只是混合
strategies in the induced normal form 归纳法则形式的策略
the definition of best response in Nash 纳什最佳反应的定义
equilibrium for imperfect information 不完美信息的平衡
extensive form games again just kind of 广泛的形式游戏再次只是一种
leverage the induced normal form and so 利用归纳的范式等等
all of those concepts that you already 您已经拥有的所有这些概念
understand from from normal form games 从普通形式的游戏中了解
carry over directly to imperfect 直接结转不完美
information games and so for example we 信息游戏，例如我们
know from Nash's theorem that a Nash 从纳什定理知道纳什
equilibrium always exists for every 每个人总是存在均衡
imperfect information extensive form 不完善的信息广泛形式
game because I can make a finite normal 游戏，因为我可以做有限的法线
form game out of it now it's going to be 从中形成形式的游戏
the case that this transformation can 这种转变可以
make the game exponentially bigger as it 使游戏成倍增长
could before even with the perfect 甚至可以做到完美
information case but for example for 信息案例，但例如
existence of equilibrium that doesn't 不存在的均衡
matter now lastly you might wonder what 现在很重要，您可能想知道
happens if I take both of these 如果我把这两个都发生
transformations that I've shown you and 我向您展示的转换和
I apply them together so for example I 我将它们一起应用，例如
could start with an imperfect 可能从不完美开始
information extensive form game make it 信息丰富的游戏形式
into a normal form game and then make 变成普通形式的游戏，然后制作
that back into an imperfect information 回到不完美的信息
extensive form game again so you might 再次进行广泛的形式游戏，因此您可能
wonder do I end up with the same game 我不知道我最终会玩同样的游戏吗
and the answer is no I won't because I 答案是不，我不会，因为我
might have a game tree which is pretty 可能有一个漂亮的游戏树
deep and it could have all kinds of 深，它可能有各种各样的
different equivalence classes it could 可以使用的不同等价类
have all kinds of different sequential 有各种不同的顺序
moves by the different players and when 由不同玩家移动，以及何时
I make it into a normal form game I'm 我把它变成普通的形式游戏
going to get this flat table and then 要得到这张桌子，然后
when I take a flat table and turn that 当我拿一张平桌子转身
into an extensive form game it's going 进入广泛的形式游戏
to be an extensive form game that only 成为一个广泛的形式游戏，
has two levels with all this stuff in 有两个级别的所有这些东西
one big equivalence class and so it's 一个大等价类，所以
going to be an extensive form game that 将是一个广泛的形式游戏，
looks different from the one that I 看起来和我的不同
started with but what is important is 首先开始，但重要的是
that it's going to have the same 它将具有相同的
strategy spaces the same sets of pure 策略空间相同的纯集合
strategies from both agents and it's 两家代理商的策略，
going to have the same set of Nash 将具有相同的纳什集
equilibria so although these games might 平衡，所以尽管这些游戏可能
look different from the perspective of 从不同的角度看
how they explicitly talk about time 他们如何明确谈论时间
they're going to be strategically 他们将在战略上
equivalent games and that's it for this 等效的游戏，仅此而已
video 视频