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经济博弈论12

2010-07-28 43页 pdf 396KB 19阅读

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经济博弈论12 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. ...
经济博弈论12
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…… 2 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. 3 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 4 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. 5 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 6 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. 7 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). 8 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. 9 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) 10 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. 13 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. 14 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. 17 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. 18 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. 19 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. 20 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. 21 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. 22 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. 23 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. 24 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. 25 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. 26 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
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