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1、 Unit OneMathematicsText A Game TheoryBackground Information Text OrganizationLanguage StudyFurther Reading and Practice Interests8/22/20243Unit One MathematicsBackground Information8/22/20244Unit One MathematicsAvinash Dixit and Barry Nalebuff 8/22/20245Unit One MathematicsAvinash Dixit and Barry N
2、alebuff Avinash Dixit is the John J. Sherred Professor of Economics at Princeton University. Barry Nalebuff is Milton Steinbach Professor of Management at Yale University, School of Organization and Management.8/22/20246Unit One Mathematics Game TheoryGame theory is the mathematical analysis of any
3、situation involving a conflict of interest, with the intent of indicating the optimal choices that, under given conditions, will lead to a desired outcome. Although game theory has roots in the study of such well-known amusements as checkers, tick-tack-toe, and pokerhence the nameit also involves mu
4、ch more serious conflicts of interest arising in such fields as sociology, economics, and political & military science. 8/22/20247Unit One Mathematics 博弈论博弈论博弈论有时也称为对策论是应用数学的一个分支, 是研究具有斗争或竞争性质现象的数学理论和方法,也是运筹学的一个重要学科。目前在社会学,生物学，经济学，国际关系，计算机科学, 政治学，军事战略和其他很多学科都有广泛的应用。 8/22/20248Unit One Mathematics Pr
5、incetonPrinceton is a city in Green Lake County, NJ, United States. 8/22/20249Unit One MathematicsPrinceton8/22/202410Unit One Mathematics Princeton University8/22/202411Unit One Mathematics Princeton University8/22/202412Unit One Mathematics Princeton UniversityPrinceton University is a coeducation
6、al private university located in Princeton, New Jersey. It is the fourth-oldest institution of higher education in the U.S. and is one of the eight Ivy League universities. Princeton has traditionally focused on undergraduate education and academic research, it now offers a large number of top-rated
7、 professional Masters degrees and PhD programs in a range of subjects. 8/22/202413Unit One MathematicsJohn von Neumann8/22/202414Unit One Mathematics John von Neumann He was a Hungarian-born American mathematician and who made contributions to quantum physics, functional analysis, set theory, econom
8、ics, computer science, topology, numerical analysis, hydrodynamics (of explosions), statistics and many other mathematical fields as one of world historys outstanding mathematicians. 8/22/202415Unit One Mathematics John von NeumannMost notably, von Neumann was a pioneer of the modern digital compute
9、r and the application of operator theory to quantum mechanics, a member of the Manhattan Project and the Institute for Advanced Study at Princeton, and creator of game theory and the concept of cellular automata. Along with Edward Teller and Stanislaw Ulam, von Neumann worked out key steps in the nu
10、clear physics involved in thermonuclear reactions and the hydrogen bomb. 8/22/202416Unit One Mathematics约翰约翰冯冯诺依曼诺依曼 (1903-1957) 匈牙利裔美国数学家, 普林斯顿大学和普林斯顿高等研究所教授,曾任研制原子弹的顾问，并参加研制计算机,被称为计算机之父,1954年成为美国原子能委员会委员.作为二十世纪最杰出的数学家之一, 他在数理逻辑, 测度论, 格论和连续几何学方面都有开创性的成果;在博弈论和控制论,力学,经济学和计算机研制等领域做出了杰出的贡献. 他同莫根施特恩合作，写
11、出博弈论和经济行为(Theory of Games and Economic Behavior, 1947)一书，这是博弈论（又称对策论）中的经典著作，使他成为数理经济学的奠基人之一。8/22/202417Unit One Mathematics tic-tac-toe Tic-tac-toe is a game in which two players alternately put crosses and circles in one of the compartments of a square grid of nine spaces; the goal is to get a row
12、of three crosses or three circles before the opponent does. 井字棋, 一种益智游戏。8/22/202418Unit One Mathematics8/22/202419Unit One MathematicsJohn Forbes Nash8/22/202420Unit One Mathematics John Forbes Nash John Forbes Nash, Jr. (born on June 13, 1928) is an American mathematician who works in game theory a
13、nd differential geometry. He shared the 1994 Nobel Prize in Economics with two other game theorists, Reinhard Selten and John Harsanyi. 8/22/202421Unit One MathematicsJohn Forbes NashHe is best known in popular culture as the s u b j e c t o f t h e Hollywood movie, A Beautiful Mind, about his mathe
14、matical g e n i u s a n d h i s s t r u g g l e s w i t h s c h i z o p h r e n i a. 8/22/202422Unit One MathematicsNash equilibriumNash equilibrium, has become the cornerstone of game theory. Nash equilibrium abstracts the way we reason about strategies in a competitive situation: it codifies I thi
15、nk he will do X because he thinks I will do Y, so I should do Z.8/22/202423Unit One Mathematics Nash equilibrium 纳什均衡，又称为非合作博弈均衡，是博弈论的一个重要术语，以约翰纳什命名。在一个博弈过程中，无论对方的策略选择如何，当事人一方都会选择某个确定的策略，则该策略被称作支配性策略。如果两个博弈的当事人的策略组合分别构成各自的支配性策略，那么这个组合就被定义为纳什均衡。一个策略组合被称为纳什均衡，当每个博弈者的均衡策略都是为了达到自己期望收益的最大值，与此同时，其他所有博弈者也遵
16、循这样的策略。8/22/202424Unit One MathematicsPrisoners DilemmaThe Prisoners Dilemma is one of the best-known models in game theory. It illustrates the paradoxical nature of interaction between mutually suspicious participants with opposing interests. 8/22/202425Unit One MathematicsPrisoners Dilemma 囚徒困境，博弈
17、论的经典案例。囚徒困境是博弈论的非零和博弈中具代表性的例子，反映个人最佳选择并非团体最佳选择。虽然困境本身只属模型性质，但现实中的价格竞争、环境保护等方面，也会频繁出现类似情况。单次发生的囚徒困境，和多次重复的囚徒困境结果不会一样。在重复的囚徒困境中，博弈被反复地进行。因而每个参与者都有机会去“惩罚”另一个参与者前一回合的不合作行为。这时，合作可能会作为均衡的结果出现。欺骗的动机这时可能被受到惩罚的威胁所克服，从而可能导向一个较好的、合作的结果。8/22/202426Unit One MathematicsHernando Corts He was the conquistador who b
18、ecame famous for leading the military expedition that initiated the Spanish Conquest of Mexico. Corts was part of the generation of European colonizers that began the first phase of the Spanish colonization of the Americas. 8/22/202427Unit One MathematicsHernando Corts8/22/202428Unit One Mathematics
19、Thomas Schelling8/22/202429Unit One MathematicsThomas Schelling8/22/202430Unit One Mathematics Thomas Schelling Thomas Crombie Schelling (born on 14 April 1921) is an American economist and professor of foreign affairs, national security, nuclear strategy, and arms control at the University of Maryl
20、and, College Park School of Public Policy. He was awarded the 2005 Nobel Prize in Economics (shared with Robert Aumann) for “having enhanced our understanding of conflict and cooperation through game theory analysis”. 8/22/202431Unit One Mathematics Thomas SchellingSchelling received his bachelors d
21、egree in economics from the University of California, Berkeley in 1944. He received his PhD in economics from Harvard University in 1951. Schellings most famous book, The Strategy of Conflict (1960), has pioneered the study of bargaining and strategic behavior and is considered one of the hundred bo
22、oks that have been most influential in the West since 1945. In this book he introduced the concept of the focal point, now commonly called the Schelling point. Schellings economic theories about war were extended in Arms and Influence (1966). 8/22/202432Unit One MathematicsWinston Churchill8/22/2024
23、33Unit One MathematicsThe Big Three8/22/202434Unit One Mathematics Winston Churchill He was the English statesman and author, best known as Prime Minister of the United Kingdom during the Second World War. Well-known as an orator, strategist, and politician, Churchill was one of the most important l
24、eaders in modern British and world history. He won the 1953 Nobel Prize in Literature for his many books on English and world history. Sir Winston Churchill was voted the greatest-ever Briton in the 2002 BBC poll the 100 Greatest Britons. 8/22/202435Unit One MathematicsText Organization Part One (Pa
25、ra. 1-3) Game theory can be defined the science of strategy which studies both pure conflicts (zero-sum games) and conflicts in cooperative forms. Part Two (Para. 4-11) There are two distinct types of strategic interdependence: sequential-move game and simultaneous-move game. 8/22/202436Unit One Mat
26、hematicsText Organization Part Three (Para. 12-19) The typical examples of game theory are given as basic principles such as prisoners dilemma, mixing moves, strategic moves, bargaining, concealing and revealing information. Part Four (Para. 20) The research of game theory has succeeded in illustrat
27、ing strategies in situations of conflict and cooperation and it will focus on the design of successful strategy in future.8/22/202437Unit One MathematicsLanguage Study8/22/202438Unit One Mathematics range (para. 1)vary between limits, extend, run in a lineThe price ranges from 30$ to 80$.The boundar
28、y ranges from north to south. takeover n. the act or an instance of assuming control or management of or responsibility for something The economy of Hongkong goes well after its takeover. 8/22/202439Unit One MathematicsGame theory was pioneered by Princeton mathematician John von Neumann. (para. 2):
29、pioneer n. original investigator of subject or explorer or settler; initiator of enterprise The young generation was greatly motivated by the pioneers exploits. The pioneers of Puritans settled down in New England. v. be a pioneer; originate (course of action etc, followed later by others)The new tr
30、eatment for cancer was pioneered by the experts of state hospital.8/22/202440Unit One MathematicsThat is, the participants were supposed to choose and implement their actions jointly. (para. 2): That is, the players were expected to select and carry out their actions together. 8/22/202441Unit One Ma
31、thematicshe must anticipate and overcome resistance to his plans. (para. 3):v. 1) deal with or use before proper time Ted was not used to saving monthly and he would always anticipate his income.2) to expect or realize beforehand, foresee The experts are anticipating the negative effects of air poll
32、ution. The directors anticipated a fall in demand/that demand would fall.8/22/202442Unit One MathematicsThe essence of a game is the interdependence of player strategies. (para. 4)essence n 1) the quality which makes a thing what it is; the inner nature or most important quality of a thing Is the es
33、sence of morality right intention? The two things are the same in outward form but different in essence. 8/22/202443Unit One Mathematics 2) extract obtained from a substance by taking out as much of the mass as possible milk essence, essence of peppermint essential adj. necessary: indispensable, mos
34、t important; fundamental Exercise, fresh air and sleep are essential for the preservation of health. Love of fair play is said to be an essential part of the English character.8/22/202444Unit One Mathematics interdependence n. the quality or fact of depending on each other interdependent adjinter-前缀
35、前缀 between each other, 类类似的词还有似的词还有interchange, intermarry, international, interview, etc.8/22/202445Unit One MathematicsIn principle, any sequential game that ends after a finite sequence of moves (para. 6):finite adj. limited; having bounds The petroleum supply is finite for humankind. infinite ad
36、j. without limits; having no bounds; (number) that cannot be calculated infinite space Atoms and molecules are infinitely small. 8/22/202446Unit One MathematicsIn contrast to the linear chain of reasoning for sequential games, a game with simultaneous moves involves a logical circle. (para. 7):A gam
37、e with simultaneous move requires a logical circular thinking, which is totally different from the linear chain of reasoning for sequential games.8/22/202447Unit One Mathematicsin ignorance of the others current actions (para. 7): ignorance n. being lacking of knowledge or uninformed The manager was
38、 offended by the ignorance of his plans. ignore v. refuse to take notice of; intentionally disregard The president ignored the rising objection against nuclear tests and insisted on carrying out the original plan. His theory contained something that was ignored in practice. 8/22/202448Unit One Mathe
39、maticsGame theory quantifies this insight and details the right proportions of such mixtures. (para. 14):insight n. piece of knowledge obtained, understanding; power of seeing into sth. with the mind a man of deep insight Good teachers have insight into the problems of students.。 show insight into h
40、uman character8/22/202449Unit One MathematicsRecall Winston Churchills dictum of hiding the truth in a “bodyguard of lies”. (para.19): recall v. 1) bring back to mind, remember something Twenty years later he could still clearly recall the event. I seem to recall seeing the document. 2) to order the
41、 return of a person who belongs to an organization The ambassador was recalled when war broke out. 8/22/202450Unit One Mathematics To convey information, use an action that is a credible “signal” (para. 19): v. make (ideas, feelings, etc.) known to another Language conveys message. Words cannot conv
42、ey how delighted I am that I have accepted by Yale University. 8/22/202451Unit One MathematicsFurther Reading8/22/202452Unit One Mathematics Further Reading IntroductoryAnkeny, Nesmith. Poker Strategy: Winning with Game Theory. 1981. Brams, Steven. Game Theory and Politics. 1979. Dixit, Avinash, and
43、 Barry Nalebuff. Thinking Strategically: A Competitive Edge in Business, Politics, and Everyday Life. 1991. McDonald, John. Strategy in Poker, Business and War. 1950. Porter, Michael. Competitive Strategy. 1982. Riker, William. The Art of Political Manipulation. 1986. Schelling, Thomas. The Strategy
44、 of Conflict. 1960. 8/22/202453Unit One Mathematics Further Reading Advanced Neumann, John von, and Oskar Morgenstern. Theory of Games and Economic Behavior. 1947. Ordeshook, Peter. Game Theory and Political Theory. 1986. Shubik, Martin. Game Theory in the Social Sciences. 1982. 8/22/202454Unit One
45、MathematicsInterests8/22/202455Unit One Mathematics What is Game Theory? (definition) Game theory is the formal study of conflict and cooperation. Game theoretic concepts apply whenever the actions of several agents are interdependent. These agents may be individuals, groups, firms, or any combinati
46、on of these. The concepts of game theory provide a language to formulate, structure, analyze, and understand strategic scenarios.8/22/202456Unit One Mathematics History of Game TheoryAntoine Cournot -the study of a duopoly (1838)Emile Borel -suggested a formal theory of games (1921) John von Neumann
47、 -publication of the monumental volume Theory of Games and Economic Behavior by John von Neumann and the economist Oskar Morgenstern (1944)8/22/202457Unit One Mathematics History of Game TheoryJohn Nash-demonstrated that finite games have always have an equilibrium point, at which all players choose
48、 actions which are best for them given their opponents choices (1950)In the 1950s and 1960s, game theory was broadened theoretically and applied to problems of war and politics. 8/22/202458Unit One Mathematics History of Game TheorySince the 1970s, it has driven a revolution in economic theory. Addi
49、tionally, it has found applications in sociology and psychology, and established links with evolution and biology. Game theory received special attention in 1994 with the awarding of the Nobel prize in economics to Nash, John Harsanyi, and Reinhard Selten.8/22/202459Unit One Mathematics Five Basic E
50、lements of Gamesplayers, or decision makers; strategies available to each player; rules governing players behavior; outcomes, each of which is a result of particular choices made by players at a given point in the game; payoffs accrued by each player as a result of each possible outcome. 8/22/202460
51、Unit One Mathematics Why is Game Theory Useful? Game theory can provide insight into the strategic options and likely outcomes available to participants in particular situations. From this insight, decision-makers can better assess the potential effects of their actions, and can make decisions that will more likely produce the desired goals and avoid conflict.8/22/202461Unit One Mathematics
