GTO2-2-05 - Transferable Utility.srt

1
00:00:00,060 --> 00:00:02,948
okay so we are now going to talk about
好的，所以我们现在要谈论

2
00:00:03,149 --> 00:00:06,309
setting which will be analyzed quite
设置将进行相当多的分析

3
00:00:06,509 --> 00:00:08,680
extensively basically for the rest of
基本上，其余的

4
00:00:08,880 --> 00:00:11,530
the course in terms of the types of
该课程的类型

5
00:00:11,730 --> 00:00:12,939
mechanisms we're going to be looking at
我们将要研究的机制

6
00:00:13,138 --> 00:00:15,280
and the alternative games we're looking
以及我们正在寻找的替代游戏

7
00:00:15,480 --> 00:00:17,320
at and in particular what this is known
特别是在什么地方

8
00:00:17,519 --> 00:00:19,629
as is a setting with transferrable
与可转让的设置一样

9
00:00:19,829 --> 00:00:25,539
utility and what's looked at in these
实用程序以及这些内容

10
00:00:25,739 --> 00:00:27,460
settings are situations where what
设置是什么情况

11
00:00:27,660 --> 00:00:30,010
people have what's known as quasi linear
人们有所谓的准线性

12
00:00:30,210 --> 00:00:34,299
preferences and the idea and before we
偏好和想法以及我们之前

13
00:00:34,500 --> 00:00:36,939
get into the formal definitions is that
进入正式定义是

14
00:00:37,140 --> 00:00:39,669
there's something like money some
有一些钱

15
00:00:39,869 --> 00:00:41,589
transferrable good that we can move back
我们可以转移的可转让商品

16
00:00:41,789 --> 00:00:44,198
and forth between agents and we know
代理商之间来回，我们知道

17
00:00:44,399 --> 00:00:47,049
that that how much that's worth to them
那对他们来说值多少钱

18
00:00:47,250 --> 00:00:48,969
and we can trade that off versus utility
我们可以权衡实用性

19
00:00:49,170 --> 00:00:53,858
and that gives us a nice sort of private
这给了我们一种很好的私人

20
00:00:54,058 --> 00:00:55,119
good that we can move back and forth
好，我们可以来回移动

21
00:00:55,320 --> 00:00:57,989
sort of payments in an auction or
拍卖中的付款方式或

22
00:00:58,189 --> 00:01:00,399
payments contributions to a public good
对公共物品的缴款

23
00:01:00,600 --> 00:01:02,588
and we'll assume that that translates
我们假设

24
00:01:02,789 --> 00:01:05,189
directly into some utility numbers and
直接放入一些实用程序编号中

25
00:01:05,390 --> 00:01:07,988
the importance of doing that is it's
这样做的重要性在于

26
00:01:08,188 --> 00:01:10,028
going to give us a lot of power in terms
将会给我们很多力量

27
00:01:10,228 --> 00:01:12,129
of aligning incentives by making
通过制定激励措施

28
00:01:12,329 --> 00:01:17,278
people's payments encapsulate the
人民付款封装了

29
00:01:17,478 --> 00:01:19,209
externalities that they're imposing on
他们施加的外部性

30
00:01:19,409 --> 00:01:21,308
others for in terms of decisions so once
其他人的决定，所以一次

31
00:01:21,509 --> 00:01:23,500
we have transferable utility it'll give
我们有可转让的实用程序

32
00:01:23,700 --> 00:01:25,689
us a lot of power and designing
我们很多力量和设计

33
00:01:25,890 --> 00:01:27,700
mechanisms in terms of making sure we
确保我们的机制

34
00:01:27,900 --> 00:01:29,799
basically price everything and we can
基本上定价一切，我们可以

35
00:01:30,000 --> 00:01:31,359
figure out what kinds of prices people
弄清楚人们的价格类型

36
00:01:31,560 --> 00:01:33,039
should be paying to change one decision
应该为改变一个决定而付出

37
00:01:33,239 --> 00:01:34,899
to another decision and that's going to
另一个决定，这将

38
00:01:35,099 --> 00:01:36,849
be a very useful tool in designing
成为设计中非常有用的工具

39
00:01:37,049 --> 00:01:39,488
mechanisms as we go forward okay so what
我们前进的机制好吗

40
00:01:39,688 --> 00:01:40,959
are the formal definitions look like
正式的定义是什么样子

41
00:01:41,159 --> 00:01:43,269
instead of just having some abstract set
而不只是设置一些抽象

42
00:01:43,469 --> 00:01:44,019
of outcomes
结果的

43
00:01:44,219 --> 00:01:45,278
now the outcomes are going to have
现在的结果将是

44
00:01:45,478 --> 00:01:47,319
structure where there will still be some
仍然会有一些结构

45
00:01:47,519 --> 00:01:50,679
some basic sort of public aspect to it
基本的公共方面

46
00:01:50,879 --> 00:01:54,668
some decision X and then the other part
一些决定X，然后是另一部分

47
00:01:54,868 --> 00:01:57,399
is going to be a set of real numbers
将是一组实数

48
00:01:57,599 --> 00:02:00,340
where we give each individual some
我们给每个人一些

49
00:02:00,540 --> 00:02:03,518
payment or may have them make up payment
付款或可以让他们补付款

50
00:02:03,718 --> 00:02:05,409
so there's some transfers going on
所以有一些转移

51
00:02:05,609 --> 00:02:07,418
between the different individuals and so
在不同的个体之间等等

52
00:02:07,618 --> 00:02:10,419
we will have some list RN of what those
我们将有一些清单RN 

53
00:02:10,618 --> 00:02:12,689
payments are so
付款是如此

54
00:02:12,889 --> 00:02:16,469
in in this particular setting when we
在这种特殊的情况下，当我们

55
00:02:16,669 --> 00:02:18,870
have quasi linear preferences so people
有准线性偏好，所以人们

56
00:02:19,069 --> 00:02:21,510
have quasi linear so here what we're
具有准线性，所以在这里

57
00:02:21,710 --> 00:02:22,650
going to have is things are going to be
将要发生的事情将是

58
00:02:22,849 --> 00:02:26,430
linear in this second dimension so we
在第二维上是线性的，所以我们

59
00:02:26,629 --> 00:02:28,170
can think of an outcome now as being a
现在可以认为结果是

60
00:02:28,370 --> 00:02:30,600
list of what's the public decision some
什么是公共决策清单

61
00:02:30,800 --> 00:02:34,560
X and a and X and then also some P which
 X和a和X然后还有一些P 

62
00:02:34,759 --> 00:02:37,680
is going to be a p1 through PN of what
通过PN成为p1 

63
00:02:37,879 --> 00:02:39,540
those payments are and a given
这些付款是给定的

64
00:02:39,740 --> 00:02:42,120
individuals utility for the outcome can
个人对结果的效用可以

65
00:02:42,319 --> 00:02:45,090
be split into a utility function which
分成一个实用函数

66
00:02:45,289 --> 00:02:47,520
describes how they like the x's and then
描述他们如何喜欢x，然后

67
00:02:47,719 --> 00:02:51,120
also they subtract off whatever payment
他们也减去任何付款

68
00:02:51,319 --> 00:02:52,740
they're making and that payment could be
他们正在付款，付款可能是

69
00:02:52,939 --> 00:02:54,240
positive or negative so it could be that
正面或负面，所以可能是

70
00:02:54,439 --> 00:02:57,020
they're paying something to into this
他们为此付出了一些代价

71
00:02:57,219 --> 00:03:01,320
society - as part of the outcome or it
社会-作为结果的一部分

72
00:03:01,520 --> 00:03:02,700
could be that they're receiving payments
可能是他们正在收款

73
00:03:02,900 --> 00:03:05,130
and these payments are going to be very
这些付款将非常

74
00:03:05,330 --> 00:03:07,680
important in designing efficient
在设计高效方面很重要

75
00:03:07,879 --> 00:03:10,050
mechanisms designing mechanisms to align
设计协调机制的机制

76
00:03:10,250 --> 00:03:12,150
people's incentives with what we'd like
人们想要的激励

77
00:03:12,349 --> 00:03:14,340
okay so quasi linearity gives us a lot
好吧，所以准线性给了我们很多

78
00:03:14,539 --> 00:03:16,230
of power you can see where the quasi
的力量，你可以看到准

79
00:03:16,430 --> 00:03:18,210
linearity where's the linearity part of
线性度是哪里的线性度

80
00:03:18,409 --> 00:03:20,910
this linearity part is that the
这个线性部分是

81
00:03:21,110 --> 00:03:22,500
Preferences are always just moving
偏好总是在变化

82
00:03:22,699 --> 00:03:24,810
linearly with whatever this payment
与这笔付款成线性关系

83
00:03:25,009 --> 00:03:27,330
scheme is whatever the money dimension
计划是金钱的任何方面

84
00:03:27,530 --> 00:03:29,310
is okay so when we start talking about
没关系，所以当我们开始谈论时

85
00:03:29,509 --> 00:03:31,650
mechanisms in this world then we can
在这个世界上的机制，那么我们可以

86
00:03:31,849 --> 00:03:34,350
split the mechanism into making a choice
将机制分解为做出选择

87
00:03:34,550 --> 00:03:36,270
so it's going to choose something so
所以要选择一些东西

88
00:03:36,469 --> 00:03:38,189
I've got our outcomes are equal to X
我得到的结果等于X 

89
00:03:38,389 --> 00:03:41,969
cross RN so what it's doing is is first
穿越RN，所以首先要做的是

90
00:03:42,169 --> 00:03:43,439
of all going to make a choice out of the
所有人将从中做出选择

91
00:03:43,639 --> 00:03:48,750
X and then also have payments in an RN
 X，然后在RN中付款

92
00:03:48,949 --> 00:03:53,219
so X and X is a non-monetary outcome and
所以X和X是非货币结果， 

93
00:03:53,419 --> 00:03:56,310
we'll use the term money here it's not
我们将在这里使用金钱一词，不是

94
00:03:56,509 --> 00:03:58,170
clear exactly what the transferable good
明确清楚什么是可转让的商品

95
00:03:58,370 --> 00:03:59,850
is but there's some way of moving
是，但是有某种方式可以移动

96
00:04:00,050 --> 00:04:02,219
something back and forth which people
来回回事的人

97
00:04:02,419 --> 00:04:05,610
can equate with utility so there's some
可以等同于效用，所以有一些

98
00:04:05,810 --> 00:04:07,469
non-monetary outcome so often these are
非货币结果，通常是

99
00:04:07,669 --> 00:04:09,660
called public decisions the aspect which
将公共决策称为

100
00:04:09,860 --> 00:04:11,130
is going to be common to all the agents
对所有代理商来说都是共同的

101
00:04:11,330 --> 00:04:14,219
and then we've got these private
然后我们将这些私人

102
00:04:14,419 --> 00:04:16,949
payments where each person is making a
每个人都在付款的地方

103
00:04:17,149 --> 00:04:20,639
payment into the mechanism and if P is
付款到机制中，如果P是

104
00:04:20,839 --> 00:04:21,838
negative then that means they're
否定则表示他们是

105
00:04:22,038 --> 00:04:24,520
actually getting a net payment to them
实际得到他们的净付款

106
00:04:24,720 --> 00:04:27,100
and the implications in terms of making
以及在制作方面的含义

107
00:04:27,300 --> 00:04:28,600
this kind of assumption in terms of
这种假设是

108
00:04:28,800 --> 00:04:31,629
these preferences first of all the
这些偏好首先

109
00:04:31,829 --> 00:04:33,699
utility that somebody has for this
有人为此提供的实用程序

110
00:04:33,899 --> 00:04:36,009
outcome can be separated out from the
结果可以与

111
00:04:36,209 --> 00:04:37,480
utility that they get from the payment
他们从付款中获得的效用

112
00:04:37,680 --> 00:04:39,670
so it's not influenced by the amount of
因此不受数量的影响

113
00:04:39,870 --> 00:04:42,370
money or wealth an agent has and second
代理人拥有的金钱或财富，其次

114
00:04:42,569 --> 00:04:46,420
secondly they people care a given agent
其次，他们会照顾给定的代理商

115
00:04:46,620 --> 00:04:49,000
cares only about X and their payment P I
只关心X及其付款PI 

116
00:04:49,199 --> 00:04:52,240
they don't care about say P J where J is
他们不在乎说PJ在哪里

117
00:04:52,439 --> 00:04:54,970
not equal to I right so they don't care
不等于我是对的，所以他们不在乎

118
00:04:55,170 --> 00:04:56,319
what payments other people are making
别人在做什么

119
00:04:56,519 --> 00:04:57,850
they just care about what's the overall
他们只是在乎整体

120
00:04:58,050 --> 00:04:59,980
decision which candidate do we pick or
决定我们选哪个候选人或

121
00:05:00,180 --> 00:05:01,509
which public good do we pick or what
我们该选择哪种公共物品？ 

122
00:05:01,709 --> 00:05:03,250
decision are we making in terms of who
我们是根据谁来做决定

123
00:05:03,449 --> 00:05:05,079
gets what good and in what payment do I
得到什么好处，我该用什么付款

124
00:05:05,279 --> 00:05:06,490
have to make and I don't care what other
必须制造，我不在乎

125
00:05:06,689 --> 00:05:08,590
people's payments are to the extent that
人们的付款范围是

126
00:05:08,790 --> 00:05:11,350
doesn't enter into my payment okay so
不能进入我的付款范围，所以

127
00:05:11,550 --> 00:05:13,420
that's the setting and then direct
那是设置，然后直接

128
00:05:13,620 --> 00:05:15,430
mechanism in this world is going to be a
这个世界上的机制将是

129
00:05:15,629 --> 00:05:19,090
combination of some choice some X theta
一些选择的组合，一些X theta 

130
00:05:19,290 --> 00:05:22,870
which comes out of X and a payment
由X和付款产生

131
00:05:23,069 --> 00:05:26,110
scheme as a function of the Thetas so
方案作为Thetas的函数

132
00:05:26,310 --> 00:05:27,730
now we announced our Thetas and then
现在我们宣布了Thetas，然后

133
00:05:27,930 --> 00:05:30,218
Society spits back at us a public
社会向我们吐口水

134
00:05:30,418 --> 00:05:32,740
decision this non-monetary decision and
决定此非货币决定，并

135
00:05:32,939 --> 00:05:35,170
then a list of transfers or payments
然后是转帐或付款清单

136
00:05:35,370 --> 00:05:36,910
that were each going to make okay so
每个都可以，所以

137
00:05:37,110 --> 00:05:41,020
that's a direct mechanism one thing
这是一种直接的机制

138
00:05:41,220 --> 00:05:42,639
that's going to be very useful in these
在这些中这将非常有用

139
00:05:42,839 --> 00:05:45,360
kinds of settings and a lot of the
各种设置以及很多

140
00:05:45,560 --> 00:05:47,829
analysis that we do going forward will
我们进行的分析将

141
00:05:48,029 --> 00:05:51,250
be in a special case of quasi linearity
在准线性的特殊情况下

142
00:05:51,449 --> 00:05:54,569
and when we're thinking about the
当我们在考虑

143
00:05:54,769 --> 00:05:57,100
utility that individuals have so we have
个人拥有的效用

144
00:05:57,300 --> 00:05:58,810
now we're writing people's utility over
现在我们在写人们的效用

145
00:05:59,009 --> 00:06:04,750
all as a utility of what the X's and the
全部用作X和

146
00:06:04,949 --> 00:06:11,170
theta minus P I of theta right so and
 theta减去theta的PI，所以

147
00:06:11,370 --> 00:06:13,540
this X can depend on theta what we're
这个X可以取决于theta我们是什么

148
00:06:13,740 --> 00:06:16,990
gonna do now is we're gonna make a look
现在要做的是我们要看看

149
00:06:17,189 --> 00:06:18,460
at situations where there's a further
在有进一步的情况

150
00:06:18,660 --> 00:06:21,218
assumption made where instead of having
假设在哪里而不是

151
00:06:21,418 --> 00:06:23,530
people's preferences depend on the full
人们的喜好取决于全部

152
00:06:23,730 --> 00:06:26,500
vector of types in the society it's
社会中类型的向量

153
00:06:26,699 --> 00:06:30,009
going to depend only on their own type
只取决于自己的类型

154
00:06:30,209 --> 00:06:32,680
so a will say that preferences have
所以会说偏好

155
00:06:32,879 --> 00:06:36,338
private values or satisfy conditional
私人价值或满足条件

156
00:06:36,538 --> 00:06:37,759
utility independence
效用独立性

157
00:06:37,959 --> 00:06:41,240
if a particular person eyes utility
如果某人眼睛有用

158
00:06:41,439 --> 00:06:45,499
function depends only on theta I okay so
功能仅取决于theta我可以，所以

159
00:06:45,699 --> 00:06:47,240
the utility for this overall outcome
总体结果的实用程序

160
00:06:47,439 --> 00:06:49,879
does not depend on anybody else's type
不取决于其他人的类型

161
00:06:50,079 --> 00:06:52,218
it only depends on my own type so that
这只取决于我自己的类型

162
00:06:52,418 --> 00:06:54,139
means that once I know my own theta I
表示一旦我知道了自己的theta 

163
00:06:54,339 --> 00:06:55,999
know everything about my preferences and
知道我的喜好和

164
00:06:56,199 --> 00:06:59,120
what this rules out is things like
排除的是类似

165
00:06:59,319 --> 00:07:01,939
investing in a stock where I'm not quite
投资我不很喜欢的股票

166
00:07:02,139 --> 00:07:03,439
sure what the value of that investment
确定那笔投资的价值

167
00:07:03,639 --> 00:07:04,819
is I don't know how well it's going to
我不知道会怎么样

168
00:07:05,019 --> 00:07:07,278
pay off and other people might have
还清，其他人可能有

169
00:07:07,478 --> 00:07:08,778
information that would be very valuable
有价值的信息

170
00:07:08,978 --> 00:07:10,999
to me that's ruled out here once I know
对我来说，一旦我知道就排除在这里

171
00:07:11,199 --> 00:07:12,829
my information I know everything I need
我的信息我知道我需要的一切

172
00:07:13,029 --> 00:07:15,468
to know about my preferences and nobody
知道我的喜好，没人

173
00:07:15,668 --> 00:07:17,290
else's information enters into that
其他信息进入

174
00:07:17,490 --> 00:07:20,990
preference calculation okay so if we're
偏好计算可以，如果我们

175
00:07:21,189 --> 00:07:23,180
talking about a particular candidate I
谈论一个特定的候选人

176
00:07:23,379 --> 00:07:24,620
know whether I like this candidate or
知道我是否喜欢这个候选人或

177
00:07:24,819 --> 00:07:26,899
not or if it's a public good I know
不是，或者我知道这是公共利益

178
00:07:27,098 --> 00:07:28,249
whether I want that cup public good
我是否想要那杯公共物品

179
00:07:28,449 --> 00:07:31,430
though so what that's what's nice about
但是，那是什么呢？ 

180
00:07:31,629 --> 00:07:34,040
the private good setting is now instead
现在改为私人物品

181
00:07:34,240 --> 00:07:36,259
of just thinking about theta eyes we can
只想着θ的眼睛

182
00:07:36,459 --> 00:07:37,879
think of just people just telling us
想到人们只是告诉我们

183
00:07:38,079 --> 00:07:39,829
what their utility function looks like
它们的效用函数是什么样的

184
00:07:40,029 --> 00:07:43,040
so we can think of the the private
所以我们可以想到私人

185
00:07:43,240 --> 00:07:45,020
information they have is just a
他们拥有的信息仅仅是

186
00:07:45,220 --> 00:07:47,870
valuation function VI of X which is
 X的估值函数VI为

187
00:07:48,069 --> 00:07:51,079
equivalent to this UI of X of theta I so
等效于theta X的用户界面，因此

188
00:07:51,279 --> 00:07:52,999
the theta just becomes telling us what
 theta只是告诉我们什么

189
00:07:53,199 --> 00:07:55,370
that function is okay so agents have a
该功能还可以，因此业务代表可以

190
00:07:55,569 --> 00:07:58,399
valuation function which is basically
估值函数基本上是

191
00:07:58,598 --> 00:08:00,620
they are the value that they have of any
它们是他们所拥有的任何价值

192
00:08:00,819 --> 00:08:04,459
particular allocation X okay and so then
特定的分配X好的，然后

193
00:08:04,658 --> 00:08:05,689
when we start thinking about direct
当我们开始考虑直接

194
00:08:05,889 --> 00:08:07,999
mechanisms we can think of the space of
我们可以想到的机制

195
00:08:08,199 --> 00:08:11,540
individuals that the private information
个人认为私人信息

196
00:08:11,740 --> 00:08:14,270
individuals have as these V is so in
个人有这样的V 

197
00:08:14,470 --> 00:08:16,040
particular everybody can tell us instead
特别是每个人都可以告诉我们

198
00:08:16,240 --> 00:08:18,139
of a type they tell us now their
他们现在告诉我们他们的类型

199
00:08:18,339 --> 00:08:20,480
valuation function and the standard
评估功能和标准

200
00:08:20,680 --> 00:08:22,819
notation we'll use is that people will
我们将使用的符号是人们会

201
00:08:23,019 --> 00:08:25,069
tell us some V hat I which might be a
告诉我们一些V帽我可能是

202
00:08:25,269 --> 00:08:25,579
lie
位于

203
00:08:25,779 --> 00:08:28,218
so dominant-strategy mechanisms they
如此重要的战略机制

204
00:08:28,418 --> 00:08:29,930
might not always exist it could be that
可能并不总是存在，可能是

205
00:08:30,129 --> 00:08:31,968
people are going to tell us some
人们会告诉我们一些

206
00:08:32,168 --> 00:08:34,399
alternate evaluation function instead of
替代评估功能代替

207
00:08:34,599 --> 00:08:36,229
the true valuation function and so we
真正的估值函数，所以我们

208
00:08:36,429 --> 00:08:37,519
can look at when is it that they're
可以看看他们什么时候

209
00:08:37,719 --> 00:08:38,659
going to want to tell us their true
要告诉我们他们的真实情况

210
00:08:38,860 --> 00:08:40,968
valuation function so now we ask people
估值功能，所以现在我们问人们

211
00:08:41,168 --> 00:08:42,799
what how do you value these different
您如何看待这些不同之处

212
00:08:43,000 --> 00:08:45,078
alternatives and under this private
替代品和这种私人

213
00:08:45,278 --> 00:08:46,609
value or conditional independent
价值或条件独立

214
00:08:46,809 --> 00:08:48,349
conditional utility independence
有条件的效用独立性

215
00:08:48,549 --> 00:08:50,569
condition they know their own
他们知道自己的条件

216
00:08:50,769 --> 00:08:51,439
preferences
首选项

217
00:08:51,639 --> 00:08:53,539
and they can tell us what that
他们可以告诉我们那

218
00:08:53,740 --> 00:08:55,339
preference function is and then we can
偏好函数是，然后我们可以

219
00:08:55,539 --> 00:08:57,139
look at mechanism design and ask it when
看一下机制设计并询问何时

220
00:08:57,339 --> 00:08:59,328
is it that possible and now this quasi
是否有可能，现在这种准

221
00:08:59,528 --> 00:09:01,758
linear world with these private values
具有这些私人价值的线性世界

222
00:09:01,958 --> 00:09:04,068
to get people to truthfully tell us what
让人们如实告诉我们

223
00:09:04,269 --> 00:09:09,269
their preferences look like
他们的喜好看起来