1
00:00:00,110 --> 00:00:04,509
let us now revisit the solution concept
现在让我们重新审视解决方案概念

2
00:00:04,710 --> 00:00:09,010
for extensive form games and let's start
进行广泛的形式游戏，让我们开始吧

3
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by doing it let's start by looking at
通过这样做，让我们开始看

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the following example in this game there
下面这个游戏中的例子

5
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are a number of Nash equilibria and here
有一些纳什均衡，这里

6
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is one of them BH see what is BH play
是其中之一BH看到BH玩什么

7
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one goes down here and down here
一个人在这里和这里下来

8
00:00:33,750 --> 00:00:38,079
whereas player two goes down here and
而第二个玩家在这里下来

9
00:00:38,280 --> 00:00:41,948
down here under this strategy profile of
在此的战略概况下

10
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course the outcome of the game is this
当然，游戏的结果是这样

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one and the payoff to both players is
一个，两个玩家的收益是

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five
五

13
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let's first convince ourselves that this
首先让我们说服自己

14
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is indeed a Nash equilibrium so let's
确实是纳什均衡，所以让我们

15
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hold players one strategy fixed and see
固定玩家一项策略，看看

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if player two can profitably deviate
如果玩家二可以有利地偏离

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from their current response well what
从他们目前的反应来看

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can they do they can say here I will
他们可以做到吗，我可以在这里说

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instead of going C I would go D they
而不是去CI会去D他们

20
00:01:13,709 --> 00:01:15,819
could say that but that would an impact
可以这么说，但这会产生影响

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the outcome at all given that player two
给那个玩家两个，结果

22
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is going down B and so that's not a
沿着B下降，所以这不是一个

23
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profitable deviation wouldn't change
盈利偏差不会改变

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their payoff the path to player two and
他们获得第二名玩家的收益， 

25
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the other thing they could do is say I'm
他们可以做的另一件事是说我

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going to go down this this way but that
这样下去，但是那

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would in fact worsen their payoff
实际上会恶化他们的收益

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because they would end up here with a
因为他们最终会在这里

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payoff of zero rather than the Pfizer
零回报而不是辉瑞

30
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getting so player 2 cannot profitably
让玩家2无法获利

31
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deviate from their current strategy what
偏离他们目前的策略是什么

32
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apply what about player player one can
适用于玩家玩家可以做什么

33
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they profitably deviate well what could
他们有利可图地偏离了什么

34
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they do they could say okay rather than
他们会说可以，而不是说

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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 

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payoff of three rather than the Pfizer
三分而不是辉瑞的回报

37
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getting that not profitable and they
得到不赚钱，他们

38
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could also say I'm going to go down G
还可以说我要去G 

39
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over here
在这里

40
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but given that player 2 is going down e
但鉴于玩家2的失败率e 

41
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that wouldn't matter though in any case
无论如何都没关系

42
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end up in this this outcome of the path
最终在这条路的这个结局中

43
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of 5 and so that's not profitable
的5，所以没有利润

44
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deviation either so neither player has a
要么偏差，要么没有球员有

45
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profitable deviation then by definition
然后根据定义获利偏差

46
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it's a Nash equilibrium but there's
这是纳什均衡，但有

47
00:02:29,120 --> 00:02:31,560
something a little disturbing about this
对此有些困扰

48
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equilibrium let's clear the slides it's
平衡让我们清除幻灯片

49
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a little less messy and let's again
少一点混乱，让我们再次

50
00:02:37,039 --> 00:02:39,570
write down the strategy for player 1
写下玩家1的策略

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00:02:39,770 --> 00:02:44,910
going be H and let's focus on Indy on
成为H，让我们专注于Indy 

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this node right there
这个节点就在那里

53
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why would player 1 actually do H because
为什么玩家1实际上会做H，因为

54
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G dominated the G they get a pair of 2
 G统治了G他们得到了一对2 

55
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rather than 1 and so even though it did
而不是1，所以即使它确实

56
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lead to a Nash equilibrium there's
导致纳什均衡

57
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something a little troubling about it
有点困扰

58
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and the way to understand it is by
而了解它的方法是

59
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claiming that they would go down H here
声称他们会在这里H下

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play 1 is threatening player 2 and
第一局威胁第二局玩家， 

61
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telling him listen do not consider going
告诉他听着不要考虑去

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down here because I'm going to go down
在这里，因为我要下去

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here therefore and you would get a zero
因此，在这里您将得到零

64
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so you'd better go here and get a 5 is
所以你最好去这里得到5分

65
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what player 1 saying is saying to player
玩家1对玩家说的是什么

66
00:03:26,539 --> 00:03:29,330
2 but this is stretch is not credible
 2，但是这是不可靠的

67
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because after all player 2 said
因为毕竟玩家2说

68
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player 1 says that but in fact it would
玩家1说，但实际上

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not be in their interests I believe that
我相信不符合他们的利益

70
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player 1 actually would go down here and
玩家1实际上会在这里下场

71
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so how do we capture this in a formal
那么我们如何在正式形式中

72
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definition that brings us to the notion
将我们带入概念的定义

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of sub game perfect equilibria or sub
子游戏完美均衡或子

74
00:03:50,479 --> 00:03:53,069
game perfection so let's first define
游戏完美，让我们先定义一下

75
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the sub game it's a very obvious notion
子游戏是一个非常明显的概念

76
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a looking at some node in the game node
看游戏节点中的某个节点

77
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H the sub game of G rooted at H is a
 H植根于H的G的子游戏是

78
00:04:04,009 --> 00:04:06,660
restricted restriction of H to this to
 H对此的限制

79
00:04:06,860 --> 00:04:10,620
the descendants from from that from that
从那个的后代

80
00:04:10,819 --> 00:04:15,840
node and similarly what are the set of
节点，类似的是什么

81
00:04:16,040 --> 00:04:18,060
all sub games of G well look at all the
 G的所有子游戏都很好看

82
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nodes in G
 G中的节点

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00:04:20,649 --> 00:04:26,389
the set of all sub games is simply all
所有子游戏的集合就是全部

84
00:04:26,589 --> 00:04:28,939
the sub game routine at some node in G
 G中某个节点的子游戏例程

85
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and so a national Librium is a sub game
因此，国家图书馆是一个子游戏

86
00:04:36,879 --> 00:04:41,600
perfect if it's restriction to every sub
如果对每个子项都有限制，则完美

87
00:04:41,800 --> 00:04:43,790
game is also a Nash equilibrium for that
博弈也是那什纳什均衡

88
00:04:43,990 --> 00:04:48,230
that sub game so if for example we go to
该子游戏，例如，如果我们去

89
00:04:48,430 --> 00:04:51,079
the previous slide and we consider again
上一张幻灯片，我们再次考虑

90
00:04:51,279 --> 00:04:54,139
clearing the slide for a second and if
清除幻灯片一秒钟，如果

91
00:04:54,339 --> 00:05:00,230
we look at the national erbium b h c e
我们看一下国家b 

92
00:05:00,430 --> 00:05:04,040
and we decide to Nash equilibrium but
然后我们决定达到纳什均衡

93
00:05:04,240 --> 00:05:07,699
among the sub games of this game the
在这个游戏的子游戏中

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00:05:07,899 --> 00:05:11,360
subtrees of this tree of this tree is
这棵树的这棵树的子树是

95
00:05:11,560 --> 00:05:13,939
this sub tree so here's a sub game it's
这个子树，所以这是一个子游戏

96
00:05:14,139 --> 00:05:15,968
a game of a single player player 1 and
单人游戏1和

97
00:05:16,168 --> 00:05:19,819
the restriction of this Nash equilibrium
纳什均衡的限制

98
00:05:20,019 --> 00:05:23,778
is simply that's action of going H but
简直就是走H的动作， 

99
00:05:23,978 --> 00:05:25,999
this is not an equilibrium in this very
这不是一个平衡

100
00:05:26,199 --> 00:05:28,730
simple tree because there's a profitable
简单的树，因为有一个有利可图的

101
00:05:28,930 --> 00:05:32,449
deviation to G for the player and so
玩家的G偏差等等

102
00:05:32,649 --> 00:05:34,218
while the to Nashville above the whole
而到纳什维尔最重要的是

103
00:05:34,418 --> 00:05:38,749
tree is restriction to the sub tree here
树是对子树的限制

104
00:05:38,949 --> 00:05:40,249
is not a Nash equilibrium
不是纳什均衡

105
00:05:40,449 --> 00:05:42,350
and therefore this Nash equilibrium is
因此，纳什均衡是

106
00:05:42,550 --> 00:05:52,550
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

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00:05:52,750 --> 00:05:54,588
that in fact that captures the intuition
实际上捕捉到了直觉

108
00:05:54,788 --> 00:05:58,310
of non-credible threat and notice also
不可信任的威胁，并且还应注意

109
00:05:58,509 --> 00:06:01,550
that one special case of the sub tree is
子树的一种特殊情况是

110
00:06:01,750 --> 00:06:04,629
the entire tree so sub game perfect
整棵树，所以子游戏完美

111
00:06:04,829 --> 00:06:06,680
equilibrium has got to also be a
平衡也必须是

112
00:06:06,879 --> 00:06:12,290
national ribbon so let's test our
国家功能区，所以让我们测试一下

113
00:06:12,490 --> 00:06:13,730
understanding of this concept a little
对这个概念有一点了解

114
00:06:13,930 --> 00:06:16,040
bit let's look at this tree and ask
让我们看看这棵树，问一下

115
00:06:16,240 --> 00:06:19,040
ourselves what are some of the sub game
我们自己是什么子游戏

116
00:06:19,240 --> 00:06:21,920
perfect equilibria there for example how
那里有完美的平衡

117
00:06:22,120 --> 00:06:28,550
about a g CF well the claim is this in
关于ag CF的说法是

118
00:06:28,750 --> 00:06:31,670
fact is sub being perfect now why is
现在事实是完美的，为什么是

119
00:06:31,870 --> 00:06:34,399
that what is a
那是什么

120
00:06:34,598 --> 00:06:44,899
G C and F so that gives you this outcome
 GC和F，以便为您提供这种结果

121
00:06:45,098 --> 00:06:48,709
over here and you can check there's no
在这里，你可以检查没有

122
00:06:48,908 --> 00:06:51,019
profitable deviation but you can also
有利可图的偏差，但您也可以

123
00:06:51,218 --> 00:06:53,778
ask in all the sub games is there
在所有子游戏中询问

124
00:06:53,978 --> 00:06:56,718
profitable deviation well let's look at
有利可图的偏差让我们来看一下

125
00:06:56,918 --> 00:06:59,209
some of the sub games well for example
例如一些子游戏

126
00:06:59,408 --> 00:07:05,600
here there is a the stevie ation over
这里有一个方向

127
00:07:05,800 --> 00:07:07,579
here but that would not be profitable
在这里，但那不会有利可图

128
00:07:07,778 --> 00:07:09,230
for pair two because they would go down
对于第二对，因为他们会下去

129
00:07:09,430 --> 00:07:16,809
from eight to three now but over here is
现在是八点到三点

130
00:07:17,009 --> 00:07:19,699
their profitable deviation for example
例如他们的利润偏差

131
00:07:19,899 --> 00:07:25,459
two player two not really because if
两个玩家两个不是真的，因为

132
00:07:25,658 --> 00:07:27,319
they deviate it over here they would end
他们在这里偏离它会结束

133
00:07:27,519 --> 00:07:29,028
up with a five random the ten they're
用五个随机数十个

134
00:07:29,228 --> 00:07:33,978
getting how about over here is their
他们在这里过得如何

135
00:07:34,178 --> 00:07:36,528
profitable deviation and this note to
有利可图的偏差和此注释

136
00:07:36,728 --> 00:07:39,468
the agent one well no because if they
该代理人很好，因为他们

137
00:07:39,668 --> 00:07:41,929
deviate they would get one rather than
偏离他们会得到一个而不是

138
00:07:42,129 --> 00:07:46,399
two so in all sub games the restriction
在所有子游戏中有两个限制

139
00:07:46,598 --> 00:07:49,429
of the strategy profile to that sub game
该子游戏的策略配置文件

140
00:07:49,629 --> 00:07:54,709
is still a Nash equilibrium and a GCF is
仍然是纳什均衡，GCF是

141
00:07:54,908 --> 00:07:56,269
in fact a sub game perfect Nash
实际上是一个完美的纳什子游戏

142
00:07:56,468 --> 00:08:03,439
equilibrium how about bhce well the
平衡怎么样？ 

143
00:08:03,639 --> 00:08:06,949
claim is that it's not well let's first
声称这不是很好，让我们先

144
00:08:07,149 --> 00:08:13,309
write down the strategy bh b h and c e
写下策略bh bh和ce 

145
00:08:13,509 --> 00:08:17,329
and this is not sub game perfect for the
这不是子游戏的完美选择

146
00:08:17,528 --> 00:08:21,160
reasons we saw before we saw that in
我们看到之前的原因

147
00:08:21,360 --> 00:08:26,540
this sub game right here there is a
这个子游戏在这里有一个

148
00:08:26,740 --> 00:08:28,480
profitable deviation for player one
玩家一的盈利偏差

149
00:08:28,680 --> 00:08:31,609
namely to deviate over here and get to
即偏离这里并到达

150
00:08:31,809 --> 00:08:34,549
rather than one and so it's not that
而不是一个，所以不是那个

151
00:08:34,750 --> 00:08:37,639
being perfect and in fact for the same
是完美的，实际上是一样的

152
00:08:37,839 --> 00:08:42,618
reason a HCF will not be sub game
 HCF不会成为子游戏的原因

153
00:08:42,818 --> 00:08:46,429
perfect let's write down what a h CF is
完美，让我们写下什么是CF 

154
00:08:46,629 --> 00:08:53,779
a h CF you can check that it's a Nash
啊CF你可以检查一下那是纳什

155
00:08:53,980 --> 00:08:59,120
equilibrium but it is a nut sub game
平衡，但这是一个疯狂的子博弈

156
00:08:59,320 --> 00:09:05,289
perfect again this sub game here is
再次完美，这里的子游戏是

157
00:09:05,490 --> 00:09:07,699
allows for profitable deviation on the
允许在

158
00:09:07,899 --> 00:09:10,909
part of the player one so even though
即使是玩家的一部分

159
00:09:11,110 --> 00:09:13,219
it's what's called off path even though
这就是所谓的偏路

160
00:09:13,419 --> 00:09:16,009
player 1 makes sure that him that he
玩家1确保他

161
00:09:16,210 --> 00:09:19,849
never gets to visit this node by going
永远不会去访问这个节点

162
00:09:20,049 --> 00:09:22,729
down here even so it's not like perfect
即使在这里也不是很完美

163
00:09:22,929 --> 00:09:26,689
because had he gotten here he would not
因为他到了这里他不会

164
00:09:26,889 --> 00:09:28,129
have done what he claims he would have
已经完成了他声称的目标

165
00:09:28,330 --> 00:09:33,529
done and that gives us a good sense for
完成，这使我们对

166
00:09:33,730 --> 00:09:34,699
what is sub game perfect Nash
什么是子游戏完美纳什

167
00:09:34,899 --> 00:09:39,899
equilibrium is
平衡是