1
集体行动博弈
Collective-Action Games
第12章
Chapter 12
Slide 2
集体行动博弈
Collective-Action Games
到目前为止,我们考虑的博弈和策略环境通常只包括
两三个相互作用的参与者。
Until now, the games and strategic situation
considered have usually included only two or
three players interacting with one another.
但是许多社会、经济和政治的相互作用都是有许多参
与者同时参加的策略环境。
But many social, economic, and political
interactions are strategic situations in which
numerous players participate at the same time.
例:职业选择,投资
,上班高峰路线选择,学习
E.g., career paths, investment plans, rush-hour
commuting routes, study……
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Slide 3
集体行动博弈
Collective-Action Games
在最一般形式中,这些多人博弈涉及到集体行动的问
。
In the most general form, such many-player
games concern problems of collective action.
如果其成员采取某一(些)特定行为,整个社会或集
体的目标可以最好地实现,但是这些行为不符合个别
成员的私人最大利益。
The aims of the whole society or collective are
best served if its members take some
particular action or actions, but these actions
are not in the best private interests of those
individual members.
Slide 4
集体行动博弈
Collective-Action Games
换句话说,社会最优结果不是作为博弈的纳什
均衡自动实现的。
In other words, the socially optimal
outcome is not automatically achievable
as the Nash equilibrium of the game.
因而我们必须考察如何修正博弈以达到社会最
优结果,或者至少改进不令人满意的纳什均衡。
Therefore we must examine how the
game can be modified to lead to the
optimal outcome or at least to improve
on the unsatisfactory Nash equilibrium.
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Slide 5
集体行动博弈
Collective-Action Games
集体行动博弈有三种形式:
Collective-action games come in
three forms:
囚徒困境 The prisoners’ dilemma
小鸡博弈 Chicken
保证博弈 Assurance games
Slide 6
内容提要
Outline
两个参与者的集体行动博弈
Collective-action games with two players
大群体中的集体行动问题
Collective-action problems in large groups
思想简史
A brief history of ideas
解决集体行动问题
Solving collective-action problems
溢出或外部性
Spillovers, or externality
“救命!”:一个混合策略的小鸡博弈
“Help!”: a game of chicken with mixed
strategies
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Slide 7
两个参与者的集体行动博弈
Collective-Action Games with Two
Players
你的邻居和你(都是农民)都可以从修建一个灌溉和防洪工程中
收益。
Your neighbor and you (both are farmers) can both
benefit by constructing an irrigation and flood-control
project.
你们两个人可以共同来进行这一工程,或者其中某一人单干。
The two of you can join together to undertake this
project or one of you might do so on your own.
不过,但工程修好后,另一个人自动得到其好处。
However, after the project has been constructed, the
other automatically gets the benefit of it.
因此每个人都试图让另一个人来修。
Therefore each is tempted to leave the work to the other.
Slide 8
两个参与者的集体行动博弈
Collective-Action Games with Two
Players
这个灌溉工程有两个重要特点:
Our irrigation project has two important
characteristics:
非排他性:没有对该工程支付的人不能够被排除在
收益的享用中。
Nonexcludable: a person who has not
contributed to paying for it cannot be
prevented from enjoying the benefits.
非竞争性:任何一个人的收益不会仅因为其他人也
得到收益而减少。
Nonrival: any one person’s benefits are not
diminished by the mere fact that someone
else is also getting the benefit.
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Slide 9
两个参与者的集体行动博弈
Collective-Action Games with Two
Players
经济学家将这样的工程称为公共物品。
Economists call such a project a pure
public good.
例如,国防
E.g., national defense
相反,一个纯粹的私人物品是完全排他和竞争
的。
In contrast, a pure private good is fully
excludable and rival.
例如,一片面包
E.g, a loaf of bread
Slide 10
两个参与者的集体行动博弈
Collective-Action Games with Two
Players
0, 06, -1Not
-1, 64, 4BuildYOU
NotBuild
NEIGHBORCost (人均per capita):
alone=7/0, together=4
Benefit (per capita):
alone=6, together=8
Not building is the dominant strategy for each.
The game is a prisoners’ dilemma (Version I).
NE
Social optimum
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Slide 11
两个参与者的集体行动博弈
Collective-Action Games with Two
Players
你被称为是你邻居付出努力的搭便车者,如果
你让他做所有的工作,然后攫取完全相同的收
益。
You are said to be a free rider on your
neighbor’s effort if you let the other do
all the work and then reap the benefits
all the same.
在一个集体行动博弈中,当所有参与者的收益
的总和最大化了,“社会”最优就达到了。
The “social” optimum in a collective-
action game is achieved when the sum
total of the players’ payoffs is
maximized.
Slide 12
两个参与者的集体行动博弈
Collective-Action Games with Two
Players
参与者的纳什均衡行为通常不能带来社会最优
结果。
Nash equilibrium behavior of the
players does not regularly bring about
the socially optimal outcome.
纳什均衡和社会最优的分歧出现在所有形式的
集体行动博弈中。
The divergence between Nash
equilibrium and socially optimum
outcomes appears in every version of
collective-action games.
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Slide 13
两个参与者的集体行动博弈
Collective-Action Games with Two
Players
0, 06, -1Not
-1, 62.3, 2.3BuildYOU
NotBuild
NEIGHBORCost (per capita):
alone=7/0, together=4
Benefit (per capita):
alone=6, together=6.3
NESO
Still a prisoners’ dilemma(Version II).
Slide 14
两个参与者的集体行动博弈
Collective-Action Games with Two
Players
0, 06, 2Not
2, 65, 5BuildYOU
NotBuild
NEIGHBORCost (per capita):
alone=4/0, together=3
Benefit (per capita):
alone=6, together=8
NESO
This is a Chicken game (version I).
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Slide 15
两个参与者的集体行动博弈
Collective-Action Games with Two
Players
0, 06, 2Not
2, 62.3, 2.3BuildYOU
NotBuild
NEIGHBORCost (per capita):
alone=4/0, together=3
Benefit (per capita):
alone=6, together=6.3
NE & SO
Still a Chicken game (Version II).
Slide 16
两个参与者的集体行动博弈
Collective-Action Games with Two
Players
0, 03, -4Not
-4, 34, 4BuildYOU
NotBuild
NEIGHBORCost (per capita):
alone=7/0, together=4
Benefit (per capita):
alone=3, together=8
NESOThis is an Assurance game.
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Slide 17
大群体中的集体行动问题
Collective-Action Problems in Large
Groups
一个有N个农民的群体中每个人都必须决定是否参加灌
溉工程的建设。 A
population of N farmers must each decide
whether to participate the irrigation-project.
如果他们当中有n个人参加,每个参加者的成本为c(n)。
If n of them participate, each of the
participants incurs a cost c that depends on
the number n ; so we write it as the function
c(n).
同样,群体中每个人,无论是否做贡献,都得到一个
收益b(n)。
Also, each person in the population, whether a
contributor or not, enjoys a benefit from its
completion that also is a function of n ; we
write the benefit function as b(n).
Slide 18
大群体中的集体行动问题
Collective-Action Problems in Large
Groups
因而,每个参加者的收益为,
Thus each participant gets the
payoff,
p(n) ≡ b(n)-c(n)
每个非参加者(或称逃避者)的收益为,
Whereas each nonparticipant, or
shirker, gets the payoff,
s(n) ≡ b(n)
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Slide 19
大群体中的集体行动问题
Collective-Action Problems in Large
Groups
假设你在考虑是参加还是逃避。
Suppose you are contemplating whether
to participate or to shirk.
你的最优反应规则依赖于群体中其他人中参加
者的数量。与其他无关!
Your best response rule depends on the
numbers of participants of others in the
group, and nothing else!
假定其他N-1个人参与者中包括n个参加者和
(N-n-1)个逃避者。
Suppose the other (N-1) players
consists of n participants and (N-1-n)
shirkers.
Slide 20
大群体中的集体行动问题
Collective-Action Problems in Large
Groups
如果你决定逃避,收益为s(n);
If you decide to shirk, you get a payoff
of s(n);
如果参加,收益为p(n+1)。
If you decide to participate, you get
p(n+1).
你将参加,如果,
You will participate if,
p(n+1)>s(n),
逃避,如果,
and you will shirk if,
p(n+1)
p(n+1)……
3. You should always
choose to shirk.
1.Suppose there are n
participants among others……
n
Shirking is your dominant strategy. The equilibrium entails
everyone shirking.
Since p(N)>s(0), this is a game of prisoners’ dilemma.
Slide 24
大群体中的集体行动问题
Collective-Action Problems in Large
Groups
不过,每个人都参加会更好,不自动意味着完全参加
是社会最优的。
However, the fact that each person would be
better off if everyone participated does not
automatically imply that full participation is
the best thing for society.
可能最优的是让某些人逃避。
It may be best to let some people shirk.
这样的结果会产生收益的不平等——逃避者比参加者
更好——这增加了社会解决困境的难度。
This type of outcome creates an inequality in
the payoffs – the shirkers fare better than the
participants – which adds another difficulty to
society’s attempts to revolve the dilemma.
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Slide 25
大群体中的集体行动问题
Collective-Action Problems in Large
Groups
0 N-1n →
s(n)
p(n+1)
If few others are participating,
your choice is to participate.
If many others are
participating, your choice
is to shirk.Nash equilibrium
number of participants
This is a Chicken case.
Slide 26
大群体中的集体行动问题
Collective-Action Problems in Large
Groups
社会最优的参加者数量甚至可能比纳什
均衡数量还要低。
The socially optimal number of
participants could even be smaller
than that in the Nash equilibrium.
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Slide 27
大群体中的集体行动问题
Collective-Action Problems in Large
Groups
0 N-1n →
p(n+1)
s(n)
If few others are participating,
your choice is to shirk.
This game has two Nash equilibria at the two extremes:
either everyone shirks or everyone participates. The right-
hand extreme equilibrium is the better one for society.
N-1
If many others are
participating, your choice
is to participate.
This is an Assurance game.
Slide 28
大群体中的集体行动问题
Collective-Action Problems in Large
Groups
当群体中的总人数N非常大,而且每个人只会引起很小
的差别,则对于任意的n:
When the total number of people in the group,
N, is very large, and any one person makes
only a small difference, then, for any n,
p(n+1)≈p(n)=b(n)-c(n)方法是有意识的、深思熟虑的,试图设计博弈来
解决集体行动问题。
These methods are conscious, deliberate
attempts to design the game in order to solve
the collective-action problem.
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Slide 33
保证博弈的解
Solutions for Assurance Games
在保证博弈中,社会最优结果是一个纳什均衡;问题
是同样的博弈还有另一个纳什均衡不是社会最优的。
In an assurance game, the socially optimal
outcome is a Nash equilibrium; the only
problem is that the same game has other,
socially worse, Nash equilibria.
为了达到最优的纳什均衡并同时是社会最优的结果,
只需要这一均衡成为一个焦点——也就是,保证参与
者的预期收敛到它上面。
Then all that is needed to achieve the best
Nash equilibrium and thereby the social
optimum is to make it a focal point – that is, to
ensure the convergence of the players’
expectations on it.
Slide 34
保证博弈的解
Solutions for Assurance Games
这样的收敛可以来自于习俗(或惯例),也就
是一种行为模式。它可以自动被接受,因为只
要相信其他人会做同样的事,每个人采取它是
符合个人利益的。
Such a convergence can result from a
social custom, or convention – namely, a
mode of behavior that finds automatic
acceptance because it is in everyone’s
interest to follow it so long as others
are expected to do likewise.
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Slide 35
囚徒困境的解
Solutions for Prisoners’ dilemmas
重复
Repetition
惩罚和奖励
Penalties, or rewards
领导,或“大方”
Leadership, or “big heart”
这项办法如何在大群体中起作用?
How these methods work in large
groups?
Slide 36
囚徒困境的解:重复
Solutions for Prisoners’ dilemmas:
Repetition
在重复的囚徒困境中,为了保持合作,每个参与者的头脑中都要
有这样一个预期,采取欺骗的个人收益是短暂的,很快会被一个
比合作行为更低的收益所取代。
In a repeated prisoners’ dilemma, what is needed to
maintain cooperation is the expectation in the mind of
each player that his personal benefits of cheating are
transitory and that they will quickly be replaced by a
payoff lower than that associated with cooperative
behavior.
为了使得博弈者相信从长期来看欺骗没有好处,欺骗必须能够很
快被发现,随之而来的惩罚(未来收益的减少)必须是迅速的、
确定的和使之痛苦的。
For players to believe that cheating is not beneficial
from a long-term perspective, cheating should be
detected quickly, and the punishment that follows
(reduction in future payoffs) should be sufficiently swift,
sure, and painful.
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Slide 37
囚徒困境的解:重复
Solutions for Prisoners’ dilemmas:
Repetition
一个群体相对于两个人来说有一个优势:同一对人可
能不会经常在一起相互作用,但是一个群体当中每一
个人总会和群体中的某一人相互作用。
A group has one advantage in this respect over
a pair of individual persons: the same pair may
not have occasion to interact all that
frequently, but each of them is likely to
interact with someone in the group all the time.
“去参加别人的葬礼吧,否则他们不会来参加你的。”
“ Always go to other people’s funeral.
Otherwise they won’t go to yours.” (by Yogi
Berra)
Slide 38
囚徒困境的解:重复
Solutions for Prisoners’ dilemmas:
Repetition
但是一个群体有一些不利之处:发现欺
骗和实施惩罚所要求的迅速,随着群体
人数增加而难以满足。
But a group has some
disadvantages: the required speed
and certainty of detection and
punishment suffer as the numbers
in the group increase.
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Slide 39
囚徒困境的解:惩罚和奖励
Solutions for Prisoners’ dilemmas:
Penalties and Rewards
群体当中其他成员实施的制裁通常采取的形式是取消
该人在群体未来进行的博弈中的资格。
Sanctions imposed by other members of the
group often take the form of disqualification
from future games played by the group.
一个规范通过羞耻心、负罪感和害怕其他人的反感等
形式增加了额外成本,改变了每个参与者的私人收益。
A norm changes the private payoff scale of
each player, by adding an extra cost in form of
shame, guilt, or dislike of the mere disapproval
by others.
Slide 40
囚徒困境的解:惩罚和奖励
Solutions for Prisoners’ dilemmas:
Penalties and Rewards
规范与习俗不同的是,一个人不会仅仅是因为预期其
他人会服从它,自己也就服从它;这里的额外成本是
很本质的。
Norms differ from customs in that a person
would not automatically follow the norm
merely because of the expectation that others
would follow it; the extra cost is essential.
规范和制裁也不同,如果你违反了规范,其他人并不
需要采取明显的行动来打击你;额外成本已经内在化
于你的个人收益当中。
Norms also differ from sanctions in that others
do not have to take explicit actions to hurt you
if you violate the norm; the extra cost becomes
internalized in your own payoff scale.
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Slide 41
囚徒困境的解:惩罚和奖励
Solutions for Prisoners’ dilemmas:
Penalties and Rewards
规范通过观察到社会普遍存在的对它们
的遵守而加强,对它们的经常违背而削
弱。
Norms are reinforced by
observation of society’s general
adherence to them, and they lose
their forces if they are frequently
seen to be violated.
Slide 42
对于小群体和大群体的解
Solutions in Small vs. Large group
集体行动问题成功的解决显然依赖于成功的发现欺骗和实施惩罚。
Successful solutions of collective-action problems
clearly hinges on success in detection and punishment.
作为一个规则,小群体看起来能更好地获得关于成员及其行为地
信息,因而更可能发现欺骗。
As a rule, small groups are more likely to have better
information about their members and the members’
action and therefore are more likely to be able to detect
cheating.
他们也更可能在所有成员之间沟通信息,更可能组织实施对欺骗
者的惩罚。
They are also more likely to communicate the
information to all members and more likely to organize
when inflicting punishment on a cheater.
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Slide 43
对于小群体和大群体的解
Solutions in Small vs. Large group
在许多小的村落社区成功的例子,放到
大的城市甚至国家就不可思议。
Many instances of successful
cooperation in small village
communities would be
unimaginable in a large city or
state.
Slide 44
小鸡博弈的解
Solutions for Chicken Games
对于第一类小鸡博弈(最大的社会总收
益在每个人都参加时获得)中,问题和
囚徒困境中的保持合作差不多。
For chicken version I (where the
largest total social payoff is
attained when everyone
participates), the problem is much
like that of sustaining cooperation
in the prisoners’ dilemma.
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Slide 45
小鸡博弈的解
Solutions for Chicken Games
在第二类小鸡博弈(一些人参加,允许其他人逃避)中,如果依
据习俗确立了对某一均衡的预期,那么这一均衡无需社会干预
(例如制裁)就可以维持。
In chicken II (where some participate and others are
allowed to shirk), if a custom creates the expectation of
an equilibrium, it can be maintained without further
social intervention such as sanctions.
但是,在这一均衡中,逃避者比参加者获得更高收益,这一不平
等可能产生新的问题;如果发生大的冲突或对立,整个社会的稳
定都会受到威胁。
However, in this equilibrium, the shirkers get higher
payoffs than the participants do, and this inequality can
create its own problems for the game; the conflicts and
tensions, if they are major, can threaten the whole
fabric of the society.
Slide 46
小鸡博弈的解
Solutions for Chicken Games
问题可以通过重复得到解决。参加者和逃避者的角色
可以轮流以平均化长时间内的收益。
Often the problem can be solved by repetition.
The role of participants and shirkers can be
rotated to equalize payoffs over time.
有时,问题的“解决”是通过压迫或高压政治,这使得
社会中被支配的子团体接受更低的收益,使得支配的
子团体享受更高的收益。
Some times the problem is “solved” by
oppression or coercion, which forces a
dominated subset of society to accept the
lower payoff and allows the dominant
subgroup to enjoy the higher payoffs.
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Slide 47
使得集体行动中的囚徒困境更容易解决的普遍特征
Common Features that make it easier to solve
prisoners’ dilemmas of Collective Action ……
有一个可以确认的、稳定的潜在参加者群体。
Have an identifiable and stable group of
potential participants
合作的收益足够大,使得为监督和实施合作的
规则支付的成本物有所值。
The benefits of cooperation have to be
large enough to make it worth paying
all the costs of monitoring and
enforcing the rules of cooperation
群体的成员能够相互交流。
The members of the group can
communicate with one another
Slide 48
解决集体行动问题:应用
Solving Collective-Action Problems:
Applications
一个合作的外部实施者可能不能以足够的透明
和迅速来发现欺骗或者实施惩罚。
An external enforcer of cooperation may
not be able to detect cheating or impose
punishment with sufficient clarity and
swiftness.
因而通常认为的、解决集体行动问题需要集中
的或政府政策的看法常常被证明是错误的。
Thus the frequent reaction that
centralized or government policy is
needed to solve collective-action
problems is often proved wrong.
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Slide 49
解决集体行动问题:应用
Solving Collective-Action Problems:
Applications
随着经济增长和世界贸易的扩张,我们看到了
从一个紧密联系的群体向相对疏远的贸易关系
的转变,从基于重复互动的实施向官方法律实
施的转变。
As economies grow and world trade
expands, we see a shift from tightly
linked groups to more arm’s length
trading relationships, and from
enforcement based on repeated
interactions to that of the official law.
E.g., the Maghribis vs. 热那亚 Genoese
Slide 50
解决集体行动问题:应用
Solving Collective-Action Problems:
Applications
在一个民主国家中,所有的选民有同等的政治
权利,大多数人的偏好应该是所向披靡的。
In a democracy, all voters have equal
political rights, and the majority’s
preference should prevail.
但是我们看到的很多情况并非如此。政策的效
果往往是对某些(小)团体有利,对其他人有
害。
But we see many instances in which this
does not happen. The effects of policies
are generally good for some (small)
groups and bad for others.
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Slide 51
解决集体行动问题:应用
Solving Collective-Action Problems:
Applications
为了使得自己偏爱的政策被采纳,一个团体必须采取政治行动——
游说、宣传、竞选捐款等等。
To get its preferred policy adopted, a group has to take
political action – lobbying, publicity, campaign
contributions, and so on.
为了做这些事情,该团体必须解决集体行动问题。
To do these things, the group must solve a collective-
action problem.
如果小团体更能解决这一问题上,那么政治过程产生的政策将会
反映他们的偏好,既是其他未能组织起来的团体人数更多、承受
损失大于该团体的获益。
If small groups are better able to solve this problem,
then the policies resulting from the political process will
reflect their preferences even if other groups who fail to
organize are more numerous and suffer greater losses
than the successful grou