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1、Unit One,Mathematics,Text A Game Theory,2020/7/24,Unit One Mathematics,3,Background Information,Text Organization,Language Study,Further Reading and Practice,Interests,2020/7/24,Unit One Mathematics,4,Background Information,2020/7/24,Unit One Mathematics,5,Avinash Dixit and Barry Nalebuff,2020/7/24,
2、Unit One Mathematics,6,Avinash Dixit and Barry Nalebuff,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.,2020/7/24,Unit One Mathematics,7,Game The
3、ory,Game theory is the mathematical analysis of any 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-
4、tack-toe, and pokerhence the nameit also involves much more serious conflicts of interest arising in such fields as sociology, economics, and political 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。,2020/7/24,
5、Unit One Mathematics,18,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 of three crosses or three circles before the opponent does. 井字棋, 一种益智游戏。,2020/7/24,Unit One Mathemat
6、ics,19,2020/7/24,Unit One Mathematics,20,John Forbes Nash,2020/7/24,Unit One Mathematics,21,John Forbes Nash,John Forbes Nash, Jr. (born on June 13, 1928) is an American mathematician who works in game theory and differential geometry. He shared the 1994 Nobel Prize in Economics with two other game
7、theorists, Reinhard Selten and John Harsanyi.,2020/7/24,Unit One Mathematics,22,John Forbes Nash,He is best known in popular culture as the subject of the Hollywood movie, A Beautiful Mind, about his mathematical genius and his struggles with schizophrenia.,2020/7/24,Unit One Mathematics,23,Nash equ
8、ilibrium,Nash equilibrium, has become the cornerstone of game theory. Nash equilibrium abstracts the way we reason about strategies in a competitive situation: it codifies I think he will do X because he thinks I will do Y, so I should do Z.,2020/7/24,Unit One Mathematics,24,Nash equilibrium,纳什均衡,又称
9、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循这样的策略。,2020/7/24,Unit One Mathematics,25,Prisoners Dilemma,The Prisoners Dilemma is one of the best-known models in gam
10、e theory. It illustrates the paradoxical nature of interaction between mutually suspicious participants with opposing interests.,2020/7/24,Unit One Mathematics,26,Prisoners Dilemma,囚徒困境,博弈论的经典案例。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
11、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。,2020/7/24,Unit One Mathematics,27,Hernando Corts,He was the conquistador who became famous for leading the military expedition that initiated the Spanish Conquest of Mexico. Corts was pa
12、rt of the generation of European colonizers that began the first phase of the Spanish colonization of the Americas.,2020/7/24,Unit One Mathematics,28,Hernando Corts,2020/7/24,Unit One Mathematics,29,Thomas Schelling,2020/7/24,Unit One Mathematics,30,Thomas Schelling,2020/7/24,Unit One Mathematics,31
13、,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 Maryland, College Park School of Public Policy. He was awarded the 2005 Nobel Prize in Economics (s
14、hared with Robert Aumann) for “having enhanced our understanding of conflict and cooperation through game theory analysis”.,2020/7/24,Unit One Mathematics,32,Thomas Schelling,Schelling received his bachelors degree in economics from the University of California, Berkeley in 1944. He received his PhD
15、 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 books that have been most influential in the West since 1945. In this book he introduced the
16、concept of the focal point, now commonly called the Schelling point. Schellings economic theories about war were extended in Arms and Influence (1966).,2020/7/24,Unit One Mathematics,33,Winston Churchill,2020/7/24,Unit One Mathematics,34,The Big Three,2020/7/24,Unit One Mathematics,35,Winston Church
17、ill,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 leaders in modern British and world history. He won the 1953 Nobel Prize in Litera
18、ture 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.,2020/7/24,Unit One Mathematics,36,Text Organization,Part One (Para. 1-3) Game theory can be defined the science of strategy which studies both
19、 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.,2020/7/24,Unit One Mathematics,37,Text Organization,Part Three (Para. 12-19) The typical examples of
20、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 illustrating strategies in situations of conflict and cooperation and it will focus
21、on the design of successful strategy in future.,2020/7/24,Unit One Mathematics,38,Language Study,2020/7/24,Unit One Mathematics,39,range (para. 1),vary between limits, extend, run in a line The price ranges from 30$ to 80$. The boundary ranges from north to south. takeover n. the act or an instance
22、of assuming control or management of or responsibility for something The economy of Hongkong goes well after its takeover.,2020/7/24,Unit One Mathematics,40,Game theory was pioneered by Princeton mathematician John von Neumann. (para. 2):,pioneer n. original investigator of subject or explorer or se
23、ttler; 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 treatment for cancer was pioneered by the experts of state hos
24、pital.,2020/7/24,Unit One Mathematics,41,That 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.,2020/7/24,Unit One Mathematics,42,he must anticipate and overcome resistance t
25、o 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 pollution. The directors anticipated a fall in demand/t
26、hat demand would fall.,2020/7/24,Unit One Mathematics,43,The 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 essence of morality right intention? The two thi
27、ngs are the same in outward form but different in essence.,2020/7/24,Unit One Mathematics,44,2) extract obtained from a substance by taking out as much of the mass as possible milk essence, essence of peppermint essential adj. necessary: indispensable, most important; fundamental Exercise, fresh air
28、 and sleep are essential for the preservation of health. Love of fair play is said to be an essential part of the English character.,2020/7/24,Unit One Mathematics,45,interdependence,n. the quality or fact of depending on each other interdependent adj inter-前缀 between each other, 类似的词还有interchange,
29、intermarry, international, interview, etc.,2020/7/24,Unit One Mathematics,46,In 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 adj. without limits; having no bounds; (numbe
30、r) that cannot be calculated infinite space Atoms and molecules are infinitely small.,2020/7/24,Unit One Mathematics,47,In contrast to the linear chain of reasoning for sequential games, a game with simultaneous moves involves a logical circle. (para. 7):A game with simultaneous move requires a logi
31、cal circular thinking, which is totally different from the linear chain of reasoning for sequential games.,2020/7/24,Unit One Mathematics,48,in ignorance of the others current actions (para. 7):,ignorance n. being lacking of knowledge or uninformed The manager was offended by the ignorance of his pl
32、ans. 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.,2020/7/24,Unit One Mathematics,49,Game theory quantifies this
33、 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 human character,2020/7/24,Unit On
34、e Mathematics,50,Recall 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 return of a person who belo
35、ngs to an organization The ambassador was recalled when war broke out.,2020/7/24,Unit One Mathematics,51,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 convey how delighted I am that
36、 I have accepted by Yale University.,2020/7/24,Unit One Mathematics,52,Further Reading,2020/7/24,Unit One Mathematics,53,Further Reading,Introductory Ankeny, Nesmith. Poker Strategy: Winning with Game Theory. 1981. Brams, Steven. Game Theory and Politics. 1979. Dixit, Avinash, and Barry Nalebuff. Th
37、inking 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 of Conflict. 1960.
38、,2020/7/24,Unit One Mathematics,54,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.,2020/7/24,Unit One Mathematics,55,Int
39、erests,2020/7/24,Unit One Mathematics,56,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 combination of these
40、. The concepts of game theory provide a language to formulate, structure, analyze, and understand strategic scenarios.,2020/7/24,Unit One Mathematics,57,History of Game Theory,Antoine Cournot -the study of a duopoly (1838) Emile Borel -suggested a formal theory of games (1921) John von Neumann -publication of the monumental volume Theory of Games and Economic Behavior by John von Neumann and the economist Oskar Morgenstern (1944),2020/7/24,Unit One Mathematics,58,History of Game Theory,John Nash-demonstrated
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