1、Unit 1 MathematicsWarming-upMathematics has a wide application,such as computer,economy.Now it has been broaden theoretically and applied to many social problems.It has driven a revolution in economic theory.It has also found application in sociology and psychology,and established links with evoluti
2、on and biology.One significant application is Game Theory which received special attention with the awarding of the Nobel Prize in economics to John Nash.Text A Game Theory 博弈论博弈论Game Theory Game theory is the mathematical analysis of any situation involving a conflict of interest,with the intent of
3、 indicating the optimal choices that,under given conditions,will lead to a desired outcome.It attempts to determine mathematically and logically the actions that“players”should take to secure the best outcomes for themselves in a wide array of“games”.它试图它试图以数学和逻辑的方法以数学和逻辑的方法帮助博弈者作出决策，使他帮助博弈者作出决策，使他们
4、在一系列纷繁复杂的博弈中保证利益的最大化。们在一系列纷繁复杂的博弈中保证利益的最大化。zero-sum games In game theory and economic theory,zero-sum describes a situation in which a participants gain or loss is exactly balanced by the losses or gains of the other participant(s).Examples:赌博赌博More typical are games with the potential for either mu
5、tual gain or mutual harm,as well as some conflict.更多具有代表性的例子可能会导致共同得利博弈和共更多具有代表性的例子可能会导致共同得利博弈和共同损失博弈，同样的情况还会发生在另外一些冲突中。同损失博弈，同样的情况还会发生在另外一些冲突中。Game theory was pioneered by Princeton mathematicianJohn von Neumann.更多具有代表性的例子可能会导致共同得利博弈和共同损更多具有代表性的例子可能会导致共同得利博弈和共同损失博弈，同样的情况还会发生在另外一些冲突中。失博弈，同样的情况还会发生在另
6、外一些冲突中。Princeton Princeton University is a private research university located in Princeton,New Jersey,United States.The school is one of the eight universities of the Ivy League and is considered one of the Colonial Colleges.John von Neumann A Hungarian-born American mathematics and made contributi
7、on to quantum physics,functional analysis,set theory,economics,computer science,topology,numerical analysis,hydrodynamics,statistics and may other mathematical fields as one of word historys outstanding mathematicians.When thinking about how others will respond,one must put oneself in their shoes,an
8、d think as they would;one should not impose ones own reasoning on them.在考虑其他博弈者会如何应对时，博弈者必须能设身处在考虑其他博弈者会如何应对时，博弈者必须能设身处地地换位思考，而不能把自己的主观判断强加于人。地地换位思考，而不能把自己的主观判断强加于人。tic-tac-toe 井字棋Tic-tack-toe is a pencil-and-paper game in which two players alternately put crosses(0)and circles()in one of the compar
9、tments of a square grid of nine spaces.The player who succeeds in placing three respective marks in a horizontal,vertical or diagonal row wins the game.In contrast to the linear chain of reasoning for sequential games,a game with simultaneous moves involves a logical circle.与连续策略博弈的线性思维不同，联立策略的博弈涉及与
10、连续策略博弈的线性思维不同，联立策略的博弈涉及逻辑循环。逻辑循环。John Nash John Forbes Nash Jr.(born June 13,1928)is an American mathematician and economist whose works in game theory,differential geometry,and partial differential equations have provided insight into the forces that govern chance and events inside complex systems
11、in daily life.Nash equilibrium 纳什均衡纳什均衡，又称为非合作博弈均衡又称为非合作博弈均衡 A Nash equilibrium,named after John Nash,is a set of strategies,one for each player,such that no player has incentive to unilaterally change her action.When we say that an outcome is an equilibrium,there is no presumption that each persons
12、 privately best choice will lead to a collectively optimal result.当我们把博弈的结果表述为一种均衡的时候，并不能假当我们把博弈的结果表述为一种均衡的时候，并不能假定博弈的每个参与者的个人最佳策略将带来共同的最优定博弈的每个参与者的个人最佳策略将带来共同的最优化结果。化结果。Nashs notion of equilibrium remains an incomplete solution to the problem of circular reasoning in simultaneous-move games.纳什关于均衡的
13、概念还不能完全解决联立策略博弈中逻纳什关于均衡的概念还不能完全解决联立策略博弈中逻辑循环的问题。辑循环的问题。And the dynamic process that can lead to an equilibrium is left unspecified.纳什均衡还没有清除地说明关于导致均衡的动态过程。纳什均衡还没有清除地说明关于导致均衡的动态过程。Prisoners dilemma 囚徒困境囚徒困境In game theory,the prisoners dilemma is a type of non-zero game in which two players can cooper
14、ate with or defect the other player.Prisoners dilemma Two suspects are arrested by the police.The police have insufficient evidence for a conviction,and,having separated both prisoners,visit each of them to offer the same deal.If one testifies(defects from the other)for the prosecution against the o
15、ther and the other remains silent(cooperates with the other),the betrayer goes free and the silent accomplice receives the full 8-year sentence.If both remain silent,both prisoners are sentenced to only one year in jail for a minor charge.If each betrays the other,each receives a five-year sentence.
16、Each prisoner must choose to betray the other or to remain silent.Each one is assured that the other would not know about the betrayal before the end of the investigation.If we assume that each player cares only about minimizing his or her own time in jail,how should the prisoners act?警方逮捕警方逮捕A、B两名嫌
17、疑犯，但没有足够证据指控二人入罪。于是警两名嫌疑犯，但没有足够证据指控二人入罪。于是警方分开囚禁嫌疑犯，分别和二人见面，并向双方提供以下相同的选方分开囚禁嫌疑犯，分别和二人见面，并向双方提供以下相同的选择：择：若一人认罪并作证检举对方（相关术语称若一人认罪并作证检举对方（相关术语称“背叛背叛”对方），而对方对方），而对方保持沉默，此人将即时获释，沉默者将判监保持沉默，此人将即时获释，沉默者将判监8年。年。若二人都保持沉默（相关术语称互相若二人都保持沉默（相关术语称互相“合作合作”），则二人同样判监），则二人同样判监一年。一年。若二人都互相检举（互相若二人都互相检举（互相“背叛背叛”），则二人同
18、样判监），则二人同样判监5年。年。囚徒困境假定每个参与者（即囚徒困境假定每个参与者（即“囚徒囚徒”）都是利己的，即都寻求最）都是利己的，即都寻求最大自身利益，而不关心另一参与者的利益。大自身利益，而不关心另一参与者的利益。Game theory quantifies this insight and details the right proportions of such mixtures.博弈论为提高洞察力和掌握混合性策略恰当的火候提供博弈论为提高洞察力和掌握混合性策略恰当的火候提供了参考。了参考。CortsHernn Corts was a Spanish explorer who is
19、 famous mainly for his march across Mexico and his conquering of the Aztec Empire in Mexico.strategy of brinkmanship Brinkmanship is the practice of pushing a dangerous situation to the verge of disaster in order to achieve the most advantageous outcome.It occurs in international politics,foreign po
20、licy,labour relations,and(in contemporary settings)in military strategy involving the threatened use of nuclear weapons.Thomas SchellingThomas Crombie Schelling(born 14 April 1921)is an American economist and professor of foreign affairs,national security,nuclear strategy,and arms control at the Sch
21、ool of Public Policy at University of Maryland,College Park.He was awarded the 2005 Nobel Memorial Prize in Economic Sciences(shared with Robert Aumann)for having enhanced our understanding of conflict and cooperation through game-theory analysis.Winston ChurchillHe was the English statesman and aut
22、hor,best known as Prime Minister of the United Kingdom during the WWW II.Well-known as an orator,strategist,and politician,Churchill was one the important leaders in modern British and world history.He won the 1953 Nobel Prize in Literature for his many books on English and world history.To convey i
23、nformation,use an action that is credible“signal”,something that would not be desirable if the circumstances were otherwise.For example,an extended warranty is a credible signal to the consumer that the firm believes it is producing a high-quality product.如果要公布信息，就要采用传递可信信息的策略，而且如果要公布信息，就要采用传递可信信息的策
24、略，而且形势发生变化时策略也必须相应进行改变，例如，提供形势发生变化时策略也必须相应进行改变，例如，提供长期的质量保证是企业生产高质量产品信心的显示，对长期的质量保证是企业生产高质量产品信心的显示，对于消费者来说也是一个可以信赖的信号。于消费者来说也是一个可以信赖的信号。Exercise IV Multiple Choice1.D 2.D 3.D 4.B 5.B 6.C 7.D8.A 9.B 10.DExercise V Blank Filling1.prime2.interactive3.purchasing4.journal5.enhances6.abuse7.methodology8.m
25、odeling9.preferences10.constructingExercise VI Cloze1.B 2.A 3.C 4.D 5.A 6.C 7.D 8.B 9.A 10.C 11.D 12.B 13.A 14.C 15.D 16.B 17.D18.A 19.D 20.DTranslation Practice(P.18)1.1.互赢博弈和互败博弈互赢博弈和互败博弈2.2.连续策略博弈连续策略博弈3.3.联立策略博弈联立策略博弈4.4.直线推理直线推理5.5.循环推理循环推理6.6.纳什均衡纳什均衡7.7.支配化策略支配化策略8.8.最优化结果最优化结果9.9.合作破裂合作破裂10.
26、10.边缘化策略边缘化策略Translation Practice(P.18)1.pure petition and cooperation3.s t r a t e g i c interdependence4.prisoners dilemma5.long-run loss6.tit-for-tat strategy6.tit-for-tat strategy7.mixing ones moves8.hit a passing shot cross-court or down the line9.monopoly market10.equilibrium sharesTranslation
27、 Practice(P.18)1.博弈的实质是博弈者采取策略之间的相互依博弈的实质是博弈者采取策略之间的相互依赖性。这种策略性的相互依赖表现为两个不同赖性。这种策略性的相互依赖表现为两个不同的类别：连续策略之间的相互做做以及联立策的类别：连续策略之间的相互做做以及联立策略之间的相互作用略之间的相互作用。2.当我们把博弈的结果表述为一种均衡的时候，当我们把博弈的结果表述为一种均衡的时候，并不是基于以下的假设，即博弈的每个参与者并不是基于以下的假设，即博弈的每个参与者的个人最佳策略将会带来共同的最优化结果的个人最佳策略将会带来共同的最优化结果。Translation Practice(P.18)3
28、.在一些博弈的冲突中，任何理化和计划性的在一些博弈的冲突中，任何理化和计划性的行为都会对手发现并加以利用。因此，通过采行为都会对手发现并加以利用。因此，通过采用组合性策略迷惑对手就显得非常重要。我们用组合性策略迷惑对手就显得非常重要。我们在体育运动中可以发现典型的例子在体育运动中可以发现典型的例子-比如在足球比如在足球比赛中特定情况下选择跑位或传球，在网球比比赛中特定情况下选择跑位或传球，在网球比赛中击球时选择斜线球或底线球。赛中击球时选择斜线球或底线球。4.边缘政策边缘政策“是一种故意使局势变得有些无法是一种故意使局势变得有些无法控制的策略，正是这种无法控制性可能会使另控制的策略，正是这种无法控制性可能会使另一方法接受从而迫使其妥协一方法接受从而迫使其妥协”。Translation Practice(P.18)5.当博弈的一方了解其他人所不掌握的信息时，当博弈的一方了解其他人所不掌握的信息时，他会急于隐瞒这一信息（比如牌局中所拿到的他会急于隐瞒这一信息（比如牌局中所拿到的牌），在其他一些情况下，他还会想令人信服牌），在其他一些情况下，他还会想令人信服地公开某些信息（比如公司对产品质量的承地公开某些信息（比如公司对产品质量的承诺）。在这两种情况下，诺）。在这两种情况下，“行胜于言行胜于言”是博弈是博弈者遵循的基本原则者遵循的基本原则。
