Chapter11囚徒困境和重复博弈

囚徒困境和重复博弈 The Prisoners’ Dilemma and Repeated Games第11章 Chapter 11囚徒困境 Prisoners’ Dilemma囚徒困境是这样一个博弈：每个参与者有一个 优势策略，但是，当所有参与者使用他们这一 优势策略时，所产生的均衡对于每个人的结果， 比他们都使用劣势策略反而还要差。

The prisoners’ dilemma is a game in which each player has a dominant strategy, but the equilibrium that arises when all players use their dominant strategies provides a worse outcome for every player than would arise if they all used their dominated strategies instead.Slide 2囚徒困境 Prisoners’ Dilemma本章考虑囚徒困境中的参与者是否以及如何获得和保 持对他们都有利的合作结果，克服为了自身利益而背 叛的个人激励。

In this chapter, we consider whether and how the players in a prisoners’ dilemma can attain and sustain their mutually beneficial cooperative outcome, overcoming their separate incentives to defect for individual gain. 三种解 Three categories of solutions:重复 Repetition 惩罚和奖励 Penalty and reward 领导 LeadershipSlide 3内容提要 Outline基本博弈（回顾） The Basic Game (Review) 解之一：重复 Solutions I: Repetition 解之二：惩罚和奖励 Solutions II: Penalties and Rewards 解之三：领导 Solutions III: Leadership 实验证据 Experimental Evidence 真实世界中的囚徒困境 Real-world DilemmasSlide 4基本博弈（回顾） The Basic Game (Review)WIFE Confess (Defect) Confess (Defect) HUSBAND 10 yr, 10 yr Deny (Cooperate) 1 yr, 25 yr 3 yr, 3 yrDeny 25 yr, 1 yr (Cooperate)Slide 5基本博弈（回顾） The Basic Game (Review)在任何一个囚徒困境中，总会有一个合作策略 和一个欺骗或背叛策略。

In any prisoners’ dilemma, there is always a cooperative strategy and a cheating or defecting strategy. 参与者总是可以根据其策略选择，被称作背叛 者或合作者。

Players can always be labeled, according to their choice of strategy, as either defector or cooperators.Slide 6基本博弈（回顾） The Basic Game (Review)当参与者之间不进行相互合作，他们就选择背叛，希 望以对手的损失为代价，获得个人的利益。

When the players do not cooperate with each other, they choose to defect in the hope of attaining individual gain at the rival’s expense. 囚徒困境能否以及如何解决，问题的实质在于通过非 合作（个人）的行动去实现合作（共同偏好）的结果。

The essence of the question of whether, when and how a prisoner’ dilemma can be resolved is the difficulty of achieving a cooperative (jointly preferred) outcome through noncooperative (individual) actions.Slide 7解之一：重复 Solutions I: Repetition在一个囚徒困境的重复博弈中，每个参与者担心一次 背叛会导致未来合作的崩溃。

In a repeated play of the prisoners’ dilemma, each player fears that one instance of defecting will lead to a collapse of cooperation for the future. 如果未来合作的价值很大，超过了短期内通过背叛所 获得的，那么参与者的长期个人利益自动地消除了背 叛，并不需要任何额外惩罚或第三方强制。

If the value of future cooperation is large and exceeds what can be gained in the short term by defecting, then the long-run individual interests of the players can automatically and tacitly keep them from defecting, without the need for any additional punishments or Slide 8 enforcement by third parties.定价中的囚徒困境 Prisoners’ dilemma of PricingYVONNE’S BISTRO 20 (Defect) 20 (Defect) XAVIER’S TAPAS 26 (Cooperate) 288, 288 216, 360 26 (Cooperate) 360, 216 324, 324Slide 9定价中的囚徒困境 Prisoners’ dilemma of Pricing假定两个餐馆开始处于合作状态，每个人收取高价格 $26。

Suppose that the two restaurants are initially in the cooperative mode, each charging the higher price of $26. 如果他们正常地竞争至少3个月，按照一次博弈的理论， 我们似乎就应该看到合作行为（高价格）而不是背叛 行为（低价格）。

If they competed on a regular basis for at least 3 months, it seems that we might see cooperative behavior (high prices) rather than the defecting behavior (low prices) predicted by theory for the one-shot game. 但是解实际上没有那么简单。

Slide But the solution is not actually that simple. 10有限次重复 Finite Repetition只要两个参与者之间的关系持续的时间长度固定和已知，在最后 阶段的博弈中，优势策略均衡（背叛）就会出现。

As long as the relationship between the two players lasts a fixed and known length of time, the dominantstrategy equilibrium with defecting should prevail in the last period of play. 参与者到达博弈终点时，继续合作就毫无价值，于是他们选择背 叛。

When the players arrive at the end of the game, there is never any value to continued cooperation, and so they defect. 按照反转的预测，相互背叛就会一直倒回到最开始的博弈。

Then rollback predicts mutual defecting all the way back to the very first play.Slide 11无限次重复 Infinite Repetition无论在怎样的重复博弈中，相互关系的序贯性 质意味着参与者可以采取的策略依赖于前面回 合的博弈中的行为。

In repeated games of any kind, the sequential nature of the relationship means that players can adopt strategies that depend on behavior in preceding plays of the games. 这样的策略被称为或然策略。

Such strategies are known as contingent strategies.Slide 12无限次重复 Infinite Repetition大多数或然策略都是触发策略：只要对手合作，该参 与者也合作；但对方任何背叛就会“触发”规定时间长 度的惩罚期，其间以非合作来回击。

Most contingent strategies are trigger strategies, where a player plays cooperatively as long as her rival(s) do so, but any defection on their part “triggers” a period of punishment, of specific length, in which she plays noncooperative in response. 最有名的两个触发策略是严厉策略和以牙还牙。