Main Content: UNIT 1 MATHEMATICSI.Text OrganizationParts Paragraphs Main IdeasPart One Paras. 1-3 Game theory can be defined as the science of strategywhich studies both pure conflicts (zero-sum games)and conflicts in cooperative forms.Part Two Paras. 4-11 There are two distinct types of strategicinterdependence: sequential-move game andsimultaneous-move game.Part Three Paras.12-19 The typical examples of game theory are given as the 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 inillustrating strategies in situations of conflict andcooperation and it will focus on the design ofsuccessful strategy in future.nguage PointsThe games it studies range from chess to child rearing and from tennis to takeovers.Paraphrase: The games it (game theory) studies extends from chess to child bringing-up and from tennis to handovers.range: v. to vary between limits, extend, run in a line. (1) The price ranges from $ 30 to $ 80. (2) The boundary ranges from north to south.takeover: n. the act or an instance of assuming control or management of or responsibility for sth. 接收、接管. The economy of Hongkong goes well after its takeover.Game theory was pioneered by Princeton mathematician John von Neumann. pioneer: v. to be a pioneer; to originate (course of action etc., followed later by others). The new treatment for cancer was pioneered by the experts of state hospital.pioneer: n. original investigator of subject or explorer or settler; initiator of enterprise. The young generation was greatly motivated by the pioneers’ exploits. That is, the participants were supposed to choose and implement their actionsjointly.Paraphrase: That is, the players were expected to select and carry out their actions together.… he must anticipate and overcome resistance to his plans.anticipate: v. 1) to expect or realize beforehand; to foresee. The experts are anticipating the negative effects of air pollution. anticipate: v. 2) to deal with or use before proper time 预支. Ted was not used to saving monthly and he would always anticipate his income.The essence of a game is the interdependence of player strategies. Paraphrase: The key principal of a game is that player strategies are dependent on each other.essence: the quality which makes a thing what it is; the inner nature or most important quality of a thing. The two things are the same in outward form but different in essence. essence: n. 2) extract obtained from a substance by taking out as much of the mass as possible. milk essence; essence of peppermint (椒薄荷、椒薄荷油) interdependence: n. the quality or fact of depending on each otherinter-为前缀，意为between each other, 类似的词还有interchange、intermarry、international、interview等。

A general principle for a player in a sequential-move game is to look ahead and reason back.Paraphrase: A commonly-applied rule for a participant in a sequential game is to anticipate and think logically in turn.reason: v. to form or try to reach conclusions by connected thought; to think out. (1) Man’s ability to reason makes him different from the animal. (2) I reason in this way about the matter.In principle, any sequential game that ends after a finite sequence of moves…finite: a. limited; having bounds. The petroleum supply is finite for humankind.infinite: a. without limits; having no bounds; (number that cannot be calculated). infinite space.In contrast to the linear chain of reasoning for sequential games, a game with simultaneous moves involves a logical circle.Paraphrase: A game with simultaneous move requires a logical circular thinking, which is totally different from the linear chain of reasoning forsequential games.… in ignorance of the others’ current actions.ignorance: n. being lacking of knowledge or uninformed. The manager was offended by the ignorance of his plans.The logical circle is squared …square the circle: to attempt sth. impossible 做（似乎是）不可能的事When we say that an outcome is an equilibrium, there is no presumption that each person’s privately best choice will lead to a collectively optimal result. Paraphrase: When we mention that game result is an equilibrium, there is no assurance that each player’s best choice will lead to the best effect for all the players.此句是一个复合句，when引导时间状语从句，主句there is no presumption 中又包含一个同位语从句that each person’s privately best choice will lead to a collectively optimal result，修饰presumption。