经济博弈论17

1 讨价还价 Bargaining 第17章 Chapter 17 Slide 2 讨价还价 Bargaining 人们在生活中总在进行着讨价还价： People engage in bargaining throughout their lives: „ 儿童在共用玩具和做游戏上 Children over sharing toys and playing games „ 夫妇在购房、择业和孩子上 Couples over housing, careers, child rearing, etc. „ 买卖双方在价格上 Buyers and sellers over price „ 工人和老板在工资上 Workers and bosses over wages „ 国家在相互贸易政策，或在裁军上 Countries over policies of mutual trade liberalization, or mutual arms reduction „ …… 2 Slide 3 讨价还价 Bargaining 所有的讨价还价问有两个共同点。 All bargaining situations have two things in common. 首先，参加谈判各方通过达成协议所能够产生和得到 的总收益应该比他们独立行动所能得到的个人收益之 和要大。 First, the total payoff that the parties to the negotiation are capable of creating and enjoying as a result of reaching an agreement should be greater than the sum of the individual payoffs that they could achieve separately. 其次，这不是一个零和博弈。 Second, it is not a zero-sum game. Slide 4 讨价还价 Bargaining 表面看起来是一个零和博弈：当剩余存在时，谈判就是为了瓜分 它。每个讨价还价者都试图让自己多得，而留给别人更少。 It may appear to be zero-sum: when a surplus exists, the negotiation is about how to divide it up. Each bargainer tries to get more for himself and leave less for the others. 但在这背后隐藏着一个危险，如果协议未能达成，没有人可以得 到任何一点剩余。 But behind it lies the danger that, if the agreement is not reached, no one will get any surplus at all. 这一不利于双方的结果，以及双方都要避免之的愿望，为威胁 （明显的或隐含的）创造了可能，这就使得讨价还价成为一个策 略问题。 This mutually harmful alternative, as well as both parties’ desire to avoid it, is what creates the potential for the threats –explicit and implicit – that make bargaining such a strategic matter. 3 Slide 5 讨价还价 Bargaining 在博弈论产生之前，一对一的谈判一般被认为是困难 的或甚至是没有定论的一个问题。 Before the advent of game theory, one-on-one bargaining was generally thought to be a difficult and even indeterminate problem. 对于为什么一方比另一方多得，理论家不能找到一个 有条理的解释，只好把这一结果归因于含糊不清的“讨 价还价能力”的差别上。 Theorists were not able to achieve any systematic understanding of why one party gets more than another and attributed this result to vague and inexplicable differences in “bargaining power.” Slide 6 讨价还价 Bargaining 即使是简单的纳什均衡理论也不能起作用。 Even the simple theory of Nash equilibrium does not take us any farther. „ 假定2个人分1美元。每个人同时报出其想要的数量。 Suppose two people are to split $1. Each is asked to announce what he want, simultaneously. „ 如果他们所报数量x和y加起来等于或小于1，每个人得到其所 报的量。否则一无所获。 If their announcements x and y add up to 1 or less, each get what he announced. Otherwise neither get anything. „ 那么任何一对(x,y)，只要加起来等于1，都构成了该博弈的 纳什均衡。 Then any pair (x, y) adding to 1 constitute a Nash equilibrium in this game. 4 Slide 7 讨价还价 Bargaining 一种分析途径是把讨价还价看成合作博 弈。这里，各方共同寻找和实施一个解 决，可能找一个中立的第三方来作 为执行的仲裁者。 One approach views bargaining as a cooperative game, in which the parties find and implement a solution jointly, perhaps, using a neutral third party as an arbitrator for enforcement. Slide 8 讨价还价 Bargaining 另一种分析途径将讨价还价作为一个非合作博 弈，这里，各方独立地选择策略。 The other approach views bargaining as a noncooperative game, in which the parties choose strategies separately. 我们会具体分析一个出价与还价的序贯博弈， 该博弈会导出一个确定的均衡。 We specify a sequential-move game of offer and counteroffers, which leads to a determinate equilibrium. 5 Slide 9 内容提要 Outline *纳什合作解 Nash’s cooperative solution 可变威胁的讨价还价 Variable-threat bargaining *轮流出价模型I：总价值衰减 Alternating-offers model I: total value decays 实验证据 Experimental Evidence *轮流出价模型II：不耐烦 Alternating-offers model II: impatience 讨价还价中的信息操纵 Manipulating information in bargaining 与多方和就多个事项进行讨价还价 Bargaining with many parties and issues Slide 10 纳什合作解 Nash’s Cooperative Solution 考虑两家硅谷的企业，安迪和比尔。 Imagine two Silicon Valley entrepreneurs, Andy and Bill. 安迪生产微芯片，他可以以900美元的价格卖给任何一家计算机 制造商。比尔的软件包可以以100美元的价格进行零售。 Andy produces a microchip set which he can sell to any computer manufacturer for $900. Bill has a software package that can retail for $100. 两个人凑在一起，发现他们如果生产一个软硬件的联合产品，可 以卖到3,000美元。 The two meet and realize that they can produce a combined system of hardware and software worth $3,000. 对于这每单位3,000美元的收益（或2,000美元的额外收益）， 安迪和比尔各应得多少？ Of the $3,000 revenue (or $2,000 extra revenue) from each unit, how much should go to Andy and how much to Bill? 6 Slide 11 纳什合作解 Nash’s Cooperative Solution 如果两人直接面对面地谈判，最终的协议取决于二人 的倔强和耐心。 The final agreement depends on their stubbornness or patience if they negotiate directly with each other. 如果他们试图让一个第三方来仲裁这一争端，仲裁者 的决定则取决于他对于硬件和软件相对价值的判断， 以及两个当事人在他面前陈词的表现力。 If they try to have the dispute arbitrated by a third party, the arbitrator’s decision depends on his sense of the relative value of hardware and software and on the rhetorical skill of the two principals as they present their arguments before the arbitrator. Slide 12 纳什合作解 Nash’s Cooperative Solution 假定仲裁者决定利润的分配应为4:1，安迪得4。 Suppose the arbitrator decides that the division of the profit should be 4:1 in favor of Andy. 假定安迪总收益为x，比尔为y。那么， Suppose Andy gets a total of x and Bill gets a total of y. Then, x-900=4(y-100), and x+y=3,000 then, x=2,500, y=500. 7 Slide 13 一般理论 General Theory 假定两个讨价还价者，A和B，试图瓜分总价值v，这 一总价值有且只有在他们就分配达成协议后才能得到。 Suppose two bargainers, A and B, seek to split a total value v, which they can achieve if and only if they agree on a specific division. 如果没有达成协议，A会得到a，B会得到b。称为他们 的“垫底”收益或BATNAs（对谈判协议的最佳替代）。 If no agreement is reached, A will get a and B will get b. Call these their backstop payoffs or BATNAs (best alternative to a negotiated agreement). 假定a+b1, or x>1-y, or y>1-x. 这意味着先出价者优势。 This implies the first proposer’s advantage. 然而，当出价可以在一个短时间间隔进行，r和s 足够小。则： However, when offers can be made at short intervals, r and s are small enough. Then, x=s/(r+s), y=r/(r+s) 现在x+y=1。先行者优势几乎不存在。 Now x+y=1. The first proposer’s advantage is trivial. Slide 46 轮流出价模型II：不耐烦 Alternating-Offers Model II: Impatience 注释2 Note 2: y/x=r/s. 耐心在讨价还价中具有重要作用。 The patience is an important advantage in bargaining. 这一公式也将我们对于讨价还价的非合作博弈 分析途径与纳什解的合作分析途径联系起来。 This formula also ties our noncooperative game approach to bargaining to the cooperative approach of the Nash solution. 24 Slide 47 轮流出价模型II：不耐烦 Alternating-Offers Model II: Impatience 注释3：协议仍然是立即达成的——最早 的出价就被接受，这一协议也是有效率 的。 Note 3: Agreement is once again immediate – the very first offer is accepted, thus efficient. Slide 48 讨价还价中的信息操纵 Manipulating Information in Bargaining 在现实中，我们常常在不知道对手的 BATNA或者忍耐程度时进行讨价还价； 有时我们甚至不确切地知道自己的 BATNA。 In reality, we often engage in bargaining without knowing the other side’s BATNA or degree of impatience; sometimes we do not even know our own BATNA very precisely. 25 Slide 49 讨价还价中的信息操纵 Manipulating Information in Bargaining 一个有“好”的BATNA或者好耐性的参与 者想要发出信号以向对手显示这一事实。 双方也都想进行筛选。 A player with a good BATNA or a high degree of patience wants to signal this fact to the other. And each side will also try screening. Slide 50 讨价还价中的信息操纵 Manipulating Information in Bargaining 显示自己耐性的最好方法就是做事有耐心。 The best way to signal patience is to be patient. 类似的，显示自己BATNA高的方法就是走开去。 Similarly, you can signal a high BATNA by starting to walk away. 即使你的BATNA低，你也可以做出承诺不接受低于某 一水平的出价。 Even if your BATNA is low, you may commit yourself to not accepting an offer below a certain level. „ 例如：工资谈判中的委任状 E.g., mandates in wage negotiations 26 Slide 51 讨价还价中的信息操纵 Manipulating Information in Bargaining 这些策略大多有风险。他们往往是某种边缘政策 的体现。 Most of these strategies entail some risk. They are instances of brinkmanship. 谈判破裂或罢工的威胁是一种策略性行动，目的 在于更快和更好地达成协议；然而，实际发生的 谈判破裂或罢工表明这一威胁可能“误入歧途”。 Threats of breakdown of negotiations or of strikes are strategic moves intended to achieve quicker agreement or a better deal for the player making the move; however, an actual breakdown or strike is an instance of the threat “gone wrong.” Slide 52 讨价还价中的信息操纵 Manipulating Information in Bargaining 接受某一出价比任何其他东西都更为准确地显 示了一个参与者的真实支付意愿，也就容易被 其他参与者利用。 The acceptance of an offer more accurately reveals a player’s true willingness to pay than anything else and therefore is open to exploitation by the other player. 不过，对于对方