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 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)宣传

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