gametheory1

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博弈论介绍 Game Theory

2. 生活中的“囚徒困境”例子
例子1 商家价格战例子1
出售同类产品的商家之间本来可以通过共同将价格维持在高位而获利，但实际上却是相互杀价，结果都赚不到钱。当一些商家共谋将价格抬高，消费者实际上不用着急，因为商家联合维持高价的垄断行为一般不会持久，可以等待垄断的自身崩溃，价格就会掉下来。
表2 智猪博弈小猪按按大猪等待 5,1 9, -1 等待 4,4 0,0
这个博弈大猪没有劣战略。但是，小猪有一个劣战略“按”，因为无论大猪作何选择，小猪选择“等待”是比选择“按”更好一些的战略。所以，小猪会剔除“按”，而选择“等待”；大猪知道小猪会选择“等待”，从而自己选择“按”，所以，可以预料博弈的结果是(按,等待）。这称为“ 重复剔除劣战略的占优战略均衡 ”，其中小猪的战略“等待” 占优于战略“按”，而给定小猪剔除了劣战略“按”后，大猪的战略“按”又占优于战略“等待”
表4 有补贴时的博弈空中客车开发开发波音不开发 -10,10 0, 120 不开发 100,0 0,0
这时只有一个纳什均衡，即波音公司不开发和空中客车公司开发的均衡（不开发,开发），这有利于空中客车。在这里，欧共体对空中客车的补贴就是使空中客车一定要开发（无论波音是否开发）的威胁变得可置信的一种“承诺行动”。
类似的例子还有：渤海中的鱼愈来愈少了，工业化中的大气及河流污染，森林植被的破坏等。解决公共资源过度利用的出路是政府制订相应的规制政策加强管理，如我国政府规定海洋捕鱼中，每年有一段时间的“休渔期”，此时禁止捕鱼，让小鱼苗安安静静地生长，大鱼好好地产卵，并对鱼网的网眼大小作出规定，禁用过小网眼的捕网打鱼，保护幼鱼的生存。又如在三峡库区，为了保护库区水体环境，关闭了前些年泛滥成灾的许多小造纸厂等。问题：1、为什么在城市中心道路上禁止汽车鸣喇叭？

第三节博弈论（GameTheory）

第三节博弈论(Game Theory)在国际关系的研究过程中，我们时常会运用到博弈论这样一个工具。

博弈论在英语中称之为“Game Theory”。

很多人会认为这是一种所谓的游戏理论，其实不然，我们不能把Games 与Fun 同论，而应该将博弈论称之为是一种“Strategic interaction”（策略性互动）。

“博弈”一词现如今在我们的生活中出现的已经很频繁，我们经常会听说各种类型的国家间博弈（如：中美博弈），“博弈论”已经深刻的影响了世界局势和地区局势的发展。

在iChange创设的危机联动体系中，博弈论将得到充分利用，代表也将有机会运用博弈论的知识来解决iChange 核心学术委员会设计的危机。

在这一节中，我将对博弈论进行一个初步的介绍与讨论，代表们可以从这一节中了解到博弈论的相关历史以及一些经典案例的剖析。

（请注意：博弈论的应用范围非常广泛，涵盖数学、经济学、生物学、计算机科学、国际关系、政治学及军事战略等多种学科，对博弈论案例的一些深入分析有时需要运用到高等数学知识，在本节中我们不会涉及较多的数学概念，仅会通过一些基本的数学分析和逻辑推理来方便理解将要讨论的经典博弈案例。

）3.1 从“叙利亚局势”到“零和博弈”在先前关于现实主义理论的讨论中，我们对国家间博弈已经有了初步的了解，那就是国家是有目的的行为体，他们总为了实现自己利益的最大化而选择对自己最有利的战略，其次，政治结果不仅仅只取决于一个国家的战略选择还取决于其他国家的战略选择，多种选择的互相作用，或者策略性互动会产生不同的结果。

因此，国家行为体在选择战略前会预判他国的战略。

在这样的条件下，让我们用一个简单的模型分析一下发生在2013年叙利亚局势1：叙利亚危机从2011年发展至今已经将进入第四个年头。

叙利亚危机从叙利亚政府军屠杀平民和儿童再到使用化学武器而骤然升级，以2013年8月底美国欲对叙利亚动武达到最为紧张的状态，同年9月中旬，叙利亚阿萨德政府以愿意向国际社会交出化学武器并同意立即加入《禁止化学武器公约》的态度而使得局势趋向缓和。

博弈论 Game theory (全)

博弈论 Game Theory博弈论亦名“对策论”、“赛局理论”，属应用数学的一个分支, 目前在生物学，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。

在《博弈圣经》中写到：博弈论是二人在平等的对局中各自利用对方的策略变换自己的对抗策略，达到取胜的意义。

主要研究公式化了的激励结构间的相互作用。

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。

博弈论考虑游戏中的个体的预测行为和实际行为，并研究它们的优化策略。

表面上不同的相互作用可能表现出相似的激励结构（incentive structure），所以他们是同一个游戏的特例。

其中一个有名有趣的应用例子是囚徒困境（Prisoner's dilemma）。

具有竞争或对抗性质的行为称为博弈行为。

在这类行为中，参加斗争或竞争的各方各自具有不同的目标或利益。

为了达到各自的目标和利益，各方必须考虑对手的各种可能的行动方案，并力图选取对自己最为有利或最为合理的方案。

比如日常生活中的下棋，打牌等。

博弈论就是研究博弈行为中斗争各方是否存在着最合理的行为方案，以及如何找到这个合理的行为方案的数学理论和方法。

生物学家使用博弈理论来理解和预测演化（论）的某些结果。

例如，约翰·史密斯（John Maynard Smith）和乔治·普莱斯（George R. Price）在1973年发表于《自然》杂志上的论文中提出的“evolutionarily stable strategy”的这个概念就是使用了博弈理论。

其余可参见演化博弈理论（evolutionary game theory）和行为生态学（behavioral ecology）。

博弈论也应用于数学的其他分支，如概率，统计和线性规划等。

历史博弈论思想古已有之，我国古代的《孙子兵法》就不仅是一部军事著作，而且算是最早的一部博弈论专著。

博弈论最初主要研究象棋、桥牌、赌博中的胜负问题，人们对博弈局势的把握只停留在经验上，没有向理论化发展。

英语第一章阅读 game theory 原文及翻译

都具有相互依赖的共同特征。也就是说，每个参与者的结果取决于所有人的选择（策略）。在所谓的零和游戏中，玩家的利益是完全冲突的博弈论是战略的科学。它试图从数学和逻辑上确定 “玩家”应采取的行动，以确保他们在各种“游戏”中获得最佳成果。所研究的游戏包括从国际象棋到儿童饲养，从网球到收购。但是这些游戏，所以一个人的收益总是另一个人的损失。更典型的是有相互收益（正数）或相互伤害（负数）的博弈，以及一些冲突。
The essence of a game is the interdependence of player strategies. There are two distinct types of strategic interdependence: sequential and simultaneous. In the former the players move in sequence, each aware of the others’ previous actions. In the latter the players act at the same time, each ignorant of the others’ actions.
Game theory was pioneered by Princeton mathematician john von Neumann. In the early years the emphasis was on games of pure conflict (zero-sum games). Other games were considered in a cooperative form. That is, the participants were supposed to choose and implement their actions jointly. Recent research has focused on games that are neither zero sum nor purely cooperative. In these games the players choose their actions separately, but their links to others involve elements of both competition and cooperation.

game theory 教材

Game Theory 教材一、介绍Game Theory是一种研究决策问题的数学理论，它关注的是理性行为体在面临复杂互动环境时的选择和行动。

Game Theory可以广泛应用于经济学、政治学、社会学等领域，帮助人们理解和解释现实世界的各种互动现象。

本教材旨在介绍Game Theory的基本概念、方法和应用，为读者提供一种理解和分析现实世界中复杂问题的工具。

二、内容第一章：Game Theory概述本章将介绍Game Theory的基本概念、发展历程和应用领域。

我们将探讨理性行为体的假设、互动决策的基本模式以及Game Theory 的主要研究问题。

第二章：策略博弈本章将介绍策略博弈的基本概念和方法，包括策略博弈的定义、纳什均衡、零和博弈和囚徒困境等。

我们将通过实例和分析来理解和应用这些概念和方法。

第三章：非策略博弈本章将介绍非策略博弈的基本概念和方法，包括非策略博弈的定义、优势策略和劣势策略、不完全信息博弈和拍卖理论等。

我们将通过实例和分析来理解和应用这些概念和方法。

第四章：演化博弈本章将介绍演化博弈的基本概念和方法，包括演化博弈的定义、演化稳定性和动态演化博弈等。

我们将通过实例和分析来理解和应用这些概念和方法。

第五章：应用案例本章将介绍Game Theory在经济学、政治学和社会学等领域的应用案例，包括市场交易、政治选举和社会规范等。

我们将通过案例分析和讨论来深入理解和应用Game Theory的概念和方法。

三、结论本教材旨在介绍Game Theory的基本概念、方法和应用，帮助读者理解和分析现实世界中各种复杂的互动现象。

通过阅读和实践，读者可以更好地理解和掌握Game Theory，并应用于解决现实问题中。

博弈论-game-theory-两人轮流进行游戏

g(a(k+1))=0 !
当k∞时 x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 …… g(x) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 …… 这有啥用
游戏的联合
定义：对于n个给定的公平组合博弈G1, G2, …, Gn，定义他们集的合联；合对为于G一=个G1局+G面2+x…i属+G于n.X对i，于设游F戏i(xGi)i表Байду номын сангаас示设xXi的i为后它继的局局面面集合对。于G那的么一G个的局局面面x集=合{x1X,x=2,X…1*,xXn2}*，…它*X的n（后其继中局*为面笛集卡合儿积）；
gn(x1,x2,…,xn) = g(x1)⊕g(x2)⊕…⊕g(xn)
= x1⊕x2⊕…⊕xn
经典Nim游戏
图的游戏
3
0
2 0
1
3 ⊕0 ⊕0=3
0 0
1 0
1
Anti-Nim
有n堆石子，每堆ai个，两个人轮流游戏，每次游戏者取走某一石碓中至少1枚，至多k枚的石子。谁取走最后一颗石子算谁输。
一方算输无论游戏如何进行，总可以在有限步之内结束。(the
Ending Condition)
N局面，P局面
N局面——先手必胜局面
winning for the Next player
P局面——后手必胜局面
winning for the Previous player
定义：
每一个最终局面都是P局面对于一个局面，若至少有一种操作使它变成一个P局面，
还扩展
游戏4：游戏有n堆石子，第i堆有ai枚，两人轮流进行游戏，每次游戏者可以从任意一堆取走任意多枚石子，也可以将任意的一堆石子任意的分成两堆。谁取走最后一颗石子为胜。

Mathematical Introduction to Game Theory1

GAME THEORYThomas S.FergusonUniversity of California at Los AngelesINTRODUCTION.Game theory is a fascinating subject.We all know many entertaining games,such as chess,poker,tic-tac-toe,bridge,baseball,computer games—the list is quite varied and almost endless.In addition,there is a vast area of economic games,discussed in Myerson(1991)and Kreps(1990),and the related political games,Ordeshook(1986), Shubik(1982),and Taylor(1995).The competition betweenﬁrms,the conﬂict between management and labor,theﬁght to get bills through congress,the power of the judiciary, war and peace negotiations between countries,and so on,all provide examples of games in action.There are also psychological games played on a personal level,where the weapons are words,and the payoﬀs are good or bad feelings,Berne(1964).There are biological games,the competition between species,where natural selection can be modeled as a game played between genes,Smith(1982).There is a connection between game theory and the mathematical areas of logic and computer science.One may view theoretical statistics as a two person game in which nature takes the role of one of the players,as in Blackwell and Girshick(1954)and Ferguson(1968).Games are characterized by a number of players or decision makers who interact, possibly threaten each other and form coalitions,take actions under uncertain conditions, andﬁnally receive some beneﬁt or reward or possibly some punishment or monetary loss. In this text,we present various mathematical models of games and study the phenomena that arise.In some cases,we will be able to suggest what courses of action should be taken by the players.In others,we hope simply to be able to understand what is happening in order to make better predictions about the future.As we outline the contents of this text,we introduce some of the key words and terminology used in game theory.First there is the number of players which will be denoted by n.Let us label the players with the integers1to n,and denote the set of players by N={1,2,...,n}.We study mostly two person games,n=2,where the concepts are clearer and the conclusions are more deﬁnite.When specialized to one-player, the theory is simply called decision theory.Games of solitaire and puzzles are examples of one-person games as are various sequential optimization problems found in operations research,and optimization,(see Papadimitriou and Steiglitz(1982)for example),or linear programming,(see Chv´a tal(1983)),or gambling(see Dubins and Savage(1965)).There are even things called“zero-person games”,such as the“game of life”of Conway(seeBerlekamp et al.(1982)Chap.25);once an automaton gets set in motion,it keeps going without any person making decisions.We assume throughout that there are at least two players,that is,n≥2.In macroeconomic models,the number of players can be very large, ranging into the millions.In such models it is often preferable to assume that there are an inﬁnite number of players.In fact it has been found useful in many situations to assume there are a continuum of players,with each player having an inﬁnitesimal inﬂuence on the outcome as in Aumann and Shapley(1974).(Incidentally,both authors were later to win Nobel Prizes in Economics.)In this course,we take n to beﬁnite.There are three main mathematical models or forms used in the study of games,the extensive form,the strategic form and the coalitional form.These diﬀer in the amount of detail on the play of the game built into the model.The most detail is given in the extensive form,where the structure closely follows the actual rules of the game.In the extensive form of a game,we are able to speak of a position in the game,and of a move of the game as moving from one position to another.The set of possible moves from a position may depend on the player whose turn it is to move from that position. In the extensive form of a game,some of the moves may be random moves,such as the dealing of cards or the rolling of dice.The rules of the game specify the probabilities of the outcomes of the random moves.One may also speak of the information players have when they move.Do they know all past moves in the game by the other players?Do they know the outcomes of the random moves?When the players know all past moves by all the players and the outcomes of all past random moves,the game is said to be of perfect information.Two-person games of perfect information with win or lose outcome and no chance moves are known as combi-natorial games.There is a beautiful and deep mathematical theory of such games.You mayﬁnd an exposition of it in Conway(1976)and in Berlekamp et al.(1982).Such a game is said to be impartial if the two players have the same set of legal moves from each position,and it is said to be partizan otherwise.Part I of this text contains an introduc-tion to the theory of impartial combinatorial games.For another elementary treatment of impartial games see the book by Guy(1989).We begin Part II by describing the strategic form or normal form of a game.In the strategic form,many of the details of the game such as position and move are lost;the main concepts are those of a strategy and a payoﬀ.In the strategic form,each player chooses a strategy from a set of possible strategies.We denote the strategy set or action space of player i by A i,for i=1,2,...,n.Each player considers all the other players and their possible strategies,and then chooses a speciﬁc strategy from his strategy set.All players make such a choice simultaneously,the choices are revealed and the game ends with each player receiving some payoﬀ.Each player’s choice may inﬂuence theﬁnal outcome for all the players.We model the payoﬀs as taking on numerical values.In general the payoﬀs may be quite complex entities,such as“you receive a ticket to a baseball game tomorrow when there is a good chance of rain,and your raincoat is torn”.The mathematical and philosophical justiﬁcation behind the assumption that each player can replace such payoﬀs with numerical values is discussed in the Appendix under the title,Utility Theory.Thistheory is treated in detail in the books of Savage(1954)and of Fishburn(1988).We therefore assume that each player receives a numerical payoﬀthat depends on the actions chosen by all the players.Suppose player1chooses a1∈A1,player2chooses a2∈A2,etc. and player n chooses a n∈A n.Then we denote the payoﬀto player j,for j=1,2,...,n,by f j(a1,a2,...,a n),and call it the payoﬀfunction for player j.The strategic form of a game is deﬁned then by the three objects:(1)the set,N={1,2,...,n},of players,(2)the sequence,A1,...,A n,of strategy sets of the players,and(3)the sequence,f1(a1,...,a n),...,f n(a1,...,a n),of real-valued payoﬀfunctions of the players.A game in strategic form is said to be zero-sum if the sum of the payoﬀs to the players is zero no matter what actions are chosen by the players.That is,the game is zero-sum ifnf i(a1,a2,...,a n)=0i=1for all a1∈A1,a2∈A2,...,a n∈A n.In theﬁrst four chapters of Part II,we restrict attention to the strategic form ofﬁnite,two-person,zero-sum games.Such a game is said to beﬁnite if both the strategy sets areﬁnite sets.Theoretically,such games have clear-cut solutions,thanks to a fundamental mathematical result known as the minimax theorem.Each such game has a value,and both players have optimal strategies that guarantee the value.In the last three chapters of Part II,we treat two-person zero-sum games in extensive form,and show the connection between the strategic and extensive forms of games.In particular,one of the methods of solving extensive form games is to solve the equivalent strategic form.Here,we give an introduction to Recursive Games and Stochastic Games, an area of intense contemporary development(see Filar and Vrieze(1997),Maitra and Sudderth(1996)and Sorin(2002)).In the last chapter,we investigate the problems that arise when at least one of the strategy sets of the players is an inﬁnite set.In Part III,the theory is extended to two-person non-zero-sum games.Here the situation is more nebulous.In general,such games do not have values and players do not have optimal strategies.The theory breaks naturally into two parts.There is the noncooperative theory in which the players,if they may communicate,may not form binding agreements.This is the area of most interest to economists,see Gibbons(1992), and Bierman and Fernandez(1993),for example.In1994,John Nash,John Harsanyi and Reinhard Selten received the Nobel Prize in Economics for work in this area.Such a theory is natural in negotiations between nations when there is no overseeing body to enforce agreements,and in business dealings where companies are forbidden to enter into agreements by laws concerning constraint of trade.The main concept,replacing value and optimal strategy is the notion of a strategic equilibrium,also called a Nash equilibrium.This theory is treated in theﬁrst three chapters of Part III.On the other hand,in the cooperative theory the players are allowed to form binding agreements,and so there is strong incentive to work together to receive the largest total payoﬀ.The problem then is how to split the total payoﬀbetween or among the players. This theory also splits into two parts.If the players measure utility of the payoﬀin the same units and there is a means of exchange of utility such as side payments,we say the game has transferable utility;otherwise non-transferable utility.The last chapter of Part III treat these topics.When the number of players grows large,even the strategic form of a game,though less detailed than the extensive form,becomes too complex for analysis.In the coalitional form of a game,the notion of a strategy disappears;the main features are those of a coalition and the value or worth of the coalition.In many-player games,there is a tendency for the players to form coalitions to favor common interests.It is assumed each coalition can guarantee its members a certain amount,called the value of the coalition. The coalitional form of a game is a part of cooperative game theory with transferable utility,so it is natural to assume that the grand coalition,consisting of all the players, will form,and it is a question of how the payoﬀreceived by the grand coalition should be shared among the players.We will treat the coalitional form of games in Part IV.There we introduce the important concepts of the core of an economy.The core is a set of payoﬀs to the players where each coalition receives at least its value.An important example is two-sided matching treated in Roth and Sotomayor(1990).We will also look for principles that lead to a unique way to split the payoﬀfrom the grand coalition,such as the Shapley value and the nucleolus.This will allow us to speak of the power of various members of legislatures.We will also examine cost allocation problems(how should the cost of a project be shared by persons who beneﬁt unequally from it).Related Texts.There are many texts at the undergraduate level that treat various aspects of game theory.Accessible texts that cover certain of the topics treated in this text are the books of Straﬃn(1993),Morris(1994)and Tijs(2003).The book of Owen (1982)is another undergraduate text,at a slightly more advanced mathematical level.The economics perspective is presented in the entertaining book of Binmore(1992).The New Palmgrave book on game theory,Eatwell et al.(1987),contains a collection of historical sketches,essays and expositions on a wide variety of topics.Older texts by Luce and Raiﬀa(1957)and Karlin(1959)were of such high quality and success that they have been reprinted in inexpensive Dover Publications editions.The elementary and enjoyable book by Williams(1966)treats the two-person zero-sum part of the theory.Also recommended are the lectures on game theory by Robert Aumann(1989),one of the leading scholars of theﬁeld.And last,but actuallyﬁrst,there is the book by von Neumann and Morgenstern (1944),that started the wholeﬁeld of game theory.References.Robert J.Aumann(1989)Lectures on Game Theory,Westview Press,Inc.,Boulder,Col-orado.R.J.Aumann and L.S.Shapley(1974)Values of Non-atomic Games,Princeton University Press.E.R.Berlekamp,J.H.Conway and R.K.Guy(1982),Winning Ways for your Mathe-matical Plays(two volumes),Academic Press,London.Eric Berne(1964)Games People Play,Grove Press Inc.,New York.H.Scott Bierman and Luis Fernandez(1993)Game Theory with Economic Applications,2nd ed.(1998),Addison-Wesley Publishing Co.Ken Binmore(1992)Fun and Games—A Text on Game Theory,D.C.Heath,Lexington, Mass.D.Blackwell and M.A.Girshick(1954)Theory of Games and Statistical Decisions,JohnWiley&Sons,New York.V.Chv´a tal(1983)Linear Programming,W.H.Freeman,New York.J.H.Conway(1976)On Numbers and Games,Academic Press,New York.Lester E.Dubins amd Leonard J.Savage(1965)How to Gamble If You Must:Inequal-ities for Stochastic Processes,McGraw-Hill,New York.2nd edition(1976)Dover Publications Inc.,New York.J.Eatwell,gate and P.Newman,Eds.(1987)The New Palmgrave:Game Theory, W.W.Norton,New York.Thomas S.Ferguson(1968)Mathematical Statistics–A Decision-Theoretic Approach, Academic Press,New York.J.Filar and K.Vrieze(1997)Competitive Markov Decision Processes,Springer-Verlag, New York.Peter C.Fishburn(1988)Nonlinear Preference and Utility Theory,John Hopkins Univer-sity Press,Baltimore.Robert Gibbons(1992)Game Theory for Applied Economists,Princeton University Press. Richard K.Guy(1989)Fair Game,COMAP Mathematical Exploration Series.Samuel Karlin(1959)Mathematical Methods and Theory in Games,Programming and Economics,in two vols.,Reprinted1992,Dover Publications Inc.,New York. David M.Kreps(1990)Game Theory and Economic Modeling,Oxford University Press. R.D.Luce and H.Raiﬀa(1957)Games and Decisions—Introduction and Critical Survey, reprinted1989,Dover Publications Inc.,New York.A.P.Maitra ans W.D.Sudderth(1996)Discrete Gambling and Stochastic Games,Ap-plications of Mathematics32,Springer.Peter Morris(1994)Introduction to Game Theory,Springer-Verlag,New York.Roger B.Myerson(1991)Game Theory—Analysis of Conﬂict,Harvard University Press. Peter C.Ordeshook(1986)Game Theory and Political Theory,Cambridge University Press.Guillermo Owen(1982)Game Theory2nd Edition,Academic Press.Christos H.Papadimitriou and Kenneth Steiglitz(1982)Combinatorial Optimization,re-printed(1998),Dover Publications Inc.,New York.Alvin E.Roth and Marilda A.Oliveira Sotomayor(1990)Two-Sided Matching–A Study in Game-Theoretic Modeling and Analysis,Cambridge University Press.L.J.Savage(1954)The Foundations of Statistics,John Wiley&Sons,New York. Martin Shubik(1982)Game Theory in the Social Sciences,The MIT Press.John Maynard Smith(1982)Evolution and the Theory of Games,Cambridge University Press.Sylvain Sorin(2002)A First Course on Zero-Sum Repeated Games,Math´e matiques& Applications37,Springer.Philip D.Straﬃn(1993)Game Theory and Strategy,Mathematical Association of Amer-ica.Alan D.Taylor(1995)Mathematics and Politics—Strategy,Voting,Power and Proof, Springer-Verlag,New York.Stef Tijs(2003)Introduction to Game Theory,Hindustan Book Agency,India.J.von Neumann and O.Morgenstern(1944)The Theory of Games and Economic Behavior, Princeton University Press.John D.Williams,(1966)The Compleat Strategyst,2nd Edition,McGraw-Hill,New York.。

game-theory1--博弈论-英文

/100
2
Introduction
Economic Models Game Theory Models Games Summary
This course is about …
… role of economic models … models of strategic behavior … models of social interactions
• real-life cousin Homo Sapiens
• guided by (sub)conscious psychological (irrational) drives; affected by herd instincts
• not well-defined goals
• lack of ability to achieve them, lack of motivation
/100
3
Introduction
Economic Models Game Theory Models Games Summary
Plan for Today
• Economic models
• What and Why?
• Game Theory Models
• Examples
• Games
• players, strategies, information, outcomes
• guided by emotions rather than bconomic Models Game Theory Models Games Summary
Economic Models - Problem
• models do not tell us how people truly behave people do not really maximize utility

博弈论game theory

1.2.4石头、剪刀、布
A
石头剪刀
布
石头 0，0 1，-1 -1，1
B
剪刀 -1，1 0，0 1，- 1
布
1，-1 -1，1 0，0
§1.3按局中人的数量对博弈分类
1.3.1单人博弈退化为一般的最优化问题（1）单人迷宫
入口
A左B左
0
局
A左B右
M
A
B
中
A右B左
0
人
出口（奖金M）
A右B右
0
单人迷宫
田忌上中下上下中中上下中下上下上中下中上上中下 3，-3 1，-1 1，-1 1，-1 -1，1 1，-1 上下中 1，-1 3，-3 1，-1 1，-1 1，-1 -1，1 齐中上下 1，-1 -1，1 3，-3 1，-1 1，-1 1，-1 威王中下上 -1，1 1，-1 1，-1 3，-3 1，-1 1，-1 下上中 1，-1 1，-1 1，-1 -1，1 3，-3 1，-1 下中上 1，-1 1，-1 -1，1 1，-1 1，-1 3，-3
局中人的得益（payoffs）——支付博弈结果的量化局中人在博弈中得到的效用策略组合的函数
博弈的次序（orders）局中人决策是否同时
1.1.3博弈的表示方法 (1)正规型（策略型）——Payoff Matrix
A坦 B
白不坦白
坦
白 -8，-8
0，-10
不坦白 -10，0
-1，-1
例子三人决斗，开枪射杀对手，以保存自己。命中率和
每一轮的开枪次序如下。
命中率
次序
A
30%
1
B
70%
2
C

game-theory1--博弈论-英文PPT课件

• Utility maximization - major component of a certain way of thinking, pulls together most of economic theory. More attractive and realistic alternatives failed because they did not have any interesting consequences
playersknowactionstakenotherplayersactionsknowngamesclassificationintroductioneconomicmodelsgametheorymodelsgamessummary38previewperfectinformationstaticgamesnashequilibriumdynamicgamesbackwardinduction倒推归imperfectinformationdynamicgamessubgame子博弈perfectneincompleteinformationstaticgamesauctions拍卖dynamicgamessignalinggamesclassificationintroductioneconomicmodelsgametheorymodelsgamessummaryeconomicmodelsgoodenoughapproximationrealworldmanyusefulpurposesgametheorymodelseconomicmodelssituationswheredecisionmakersinteractsummaryintroductioneconomicmodelsgametheorymodelsgamessummarystrategicgameconsistseachplayerseteachplayersetpreferencesoveractionprofilespreferencesrepresentedpayofffunctionsolvinggamesiterative重复的elimination消去strictlydominatedstrategiesnextlecturenashequilibriumnextlectureothermethodslatercoursesummaryiiintroductioneconomicmodelsgametheorymodelsgamessummary

game theory博弈论

game theory博弈论
游戏理论，也被称为博弈论，是一种研究人类决策和行为的数学框架。

它旨在理解在人类决策中存在的不确定性和竞争条件下，每个参与者的决策如何影响整个系统的结果。

从二战后的经济学开始，游戏理论已经成为经济学、政治学、心理学、哲学和博弈理论的重要研究领域。

它也成为了解决现实生活中许多社会问题的一种有力工具，例如市场竞争、调解博弈、投票、拍卖、国际贸易等。

游戏理论中的核心概念包括博弈、策略、收益和均衡等。

博弈是指参与者之间的相互作用，策略是指参与者制定的行动计划，收益是指参与者对于结果的评价，均衡是指没有参与者有动机改变他们的策略的状态。

在游戏理论中，有许多不同的博弈模型，例如零和博弈、合作博弈、非合作博弈等。

在每种模型中，参与者的决策和行为都会受到不同的影响和限制。

通过了解游戏理论，我们可以更好地理解许多人类行为的原理和动机，同时也可以更好地理解和预测许多社会问题的发展趋势。

- 1 -。

博弈论又被称为对策论（GameTheory）博弈论和经济行为

博弈论又被称为对策论（GameTheory)博弈论和经济行为本文话题：博弈论和经济行为一帆风顺协同作用博弈论策略博弈论又被称为对策论（Game Theory)目录博弈论的概念博弈论的发展博弈论的基本概念基本概念博弈论的意义纳什博弈论的原理与应用囚徒困境博弈企业博弈老三论小释老三论小释博弈论的概念博弈论又被称为对策论（GameTheory)，它是现代数学的1个新分支，也是运筹学的1个重要组成内容。

按照2005年因对博弈论的贡献而获得诺贝尔经济学奖的RobertAumann教授的说法，博弈论就是研究互动决策的理论。

所谓互动决策，即各行动方（即局中人[player]）的决策是相互影响的，每个人在决策之际必须将他人的决策纳入自己的决策考虑之中，当然也需要把别人对于自己的考虑也要纳入考虑之中……在如此迭代考虑情形进行决策，选择最有利于自己的战略(strategy)。

博弈论的应用领域十分广泛，在经济学、政治科学（国内的以及国际的）、军事战略问题、进化生物学以及当代的计算机科学等领域都已成为重要的研究和分析工具。

此外，它还与会计学、统计学、数学基础、社会心理学以及诸如认识论与伦理学等哲学分支有重要联系。

按照Aumann所撰写的《新帕尔格雷夫经济学大辞典》“博弈论”辞条的看法，标准的博弈论分析出发点是理性的，而不是心理的或社会的角度。

不过，近20年来结合心理学和行为科学、实验经济学的研究成就而对博弈论进行一定改造的行为博弈论(behavoiralgame theory )也日益兴起。

博弈论的发展博弈论思想古已有之，我国古代的《孙子兵法》就不仅是一部军事著作，而且算是最早的一部博弈论专著。

博弈论最初主要研究象棋、桥牌、赌博中的胜负问题，人们对博弈局势的把握只停留在经验上,没有向理论化发展，正式发展成一门学科则是在20世纪初。

1928年冯·诺意曼证明了博弈论的基本原理，从而宣告了博弈论的正式诞生。

1944年，冯·诺意曼和摩根斯坦共著的划时代巨著《博弈论与经济行为》将二人博弈推广到n 人博弈结构并将博弈论系统的应用于经济领域，从而奠定了这一学科的基础和理论体系。

博弈论 Game Theory

• •
信息是博弈论中重要的内容。完全博弈是指在博弈过程中，每一位博弈者对其他博弈者的特征、策略空间及收益函数有准确的信息。严格地讲，完全信息博弈是指博弈者的策略空间及策略组合下的支付，是博弈中所有博弈者的“公共知识”(Commom Knowledge)的博弈。 • 完美信息是指博弈者完全清楚到他决策时为止时, 所有其他博弈者的所有决策信息，或者说，了解博弈已进行过程的所有信息。
• 2 . 猜硬币游戏
猜方正面盖正面方反面 -1，1 1，-1 反面 1，-1 -1，1
• 3. “田忌赛马” • “田忌赛马”是我国古代一个非常有名的故事，讲的是发生在齐威王与大将田忌之间的赛马的故事。田忌在谋士孙膑的帮助下，运用谋略帮助田忌以弱胜强战胜了齐威王。这个故事讲的其实是一个很典型的博弈问题。
田上中下上中下上下中齐中上下威中下上王下上中下中上 3，-3 1，-1 1，-1 -1，1 1，-1 1，-1 上下中 1，-1 3，-3 -1，1 1，-1 1，-1 1，-1 中上下 1，-1 1，-1 3，-3 1，-1 1，-1 -1，1
忌中下上 1，-1 1，-1 1，-1 3，-3 -1，1 1，-1 下上中 -1，1 1，-1 1，-1 1，-1 3，-3 1，-1 下中上 1，-1 -1，1 1，-1 1，-1 1，-1 3，-3
•
动态博弈是指在博弈中，博弈者的行动有先后顺序（Sequential-Move），且后行动者能够观察到先行动者所选择的行动或策略,因此, 动态博弈又叫做序贯博弈。
•
2.如果按照博弈者对其他博弈者所掌握的信息的完全与完备程度进行分类，博弈可以划分为完全信息博弈（Game with Complete Information）与不完全信息的博弈（Game with Incomplete Information），以及完美信息的博弈（Game with Perfect Information）与不完美信息的博弈（Game with Imperfect Information),确定的博弈(Game of Certainty)与不确定的博弈（Game of Uncertainty),对称信息的博弈（Game of Symmetric Information）与非对称信息的博弈（Game of Asymmetric Information）等。

GAME THEORY

其次，剔除新博弈中某个参与人的严格劣策略；重复上述过程，直到只剩下唯一的策略组合。我们认为这个唯一所剩的策略组合是稳定的。
1.2.2 重复剔除的占优均衡
Definition：In a normal-form game, if for each player i , si" is i‟s dominant strategy, than we call the strategies profile (s1″, …, sn" ) the „dominantstrategy equilibrium‟.
1.2.1占优战略均衡
定义2：一个博弈G,若对博弈方i及所用s-i都有 ui (si*,s-i) > ui (si ‟,s-i)，则称si*是si ‟的严格上策， si ‟是si*的严格下策。定义3：若在博弈G中对每个博弈方i都存在策略si*是其它所有策略的严格上策,则称策略组合s*=(s1*,s2*, … ,sn*)是G的上策均衡。
In the normal-form representation of a game ,each
player simultaneously chooses a strategy, and the combination of strategies chosen by the players determines a payoff for each player. Definition: The normal-form representation of an-n-player game specifies the players‟ strategy spaces S1 , … , Sn and their payoff functions u1 ,…, un. We denote this game

Game Theory1PPT课件

❖ 在该博弈中，两博弈方为厂商1和厂商2，他们各自的策略空间为 s1=[0,p1max]和s2=[0,p2max]，其中，p1max和p2max是厂商1和厂商2能卖出产品的最高的价格，两双方的得益就是各自的利润，都是双方的价格函数：
u1 u1( p1, p2) p1q1 c1q1 ( p1 c1)q1
(a1
b1c1
d1 p2 )
和
p2
R2 (P1)
1 2B2
(a2
b2c2
d2 p1)
纳什均衡必是两反映函数的交点，即必须满足：
p
* 1
1 2b1(a1来自b1c1d1 p2* )
p2*
1 2b2
(a2
b2c2
d2 p1)
解方程组，得（p*1, p2*）为该博弈惟一的纳什均
衡。将p1*, p2*代入两得益函数则可得两厂商的均
划线法
❖ 在具有策略和利益相互依存的博弈问题中，各个博弈方的得益既取决于自己选择的策略，还与其他策略方选择的策略有关。因此博弈方在决策时必须考虑其他博弈方的存在和策略选择。依据这种思想，科学的决策思路应该是:找出自己针对其他博弈方每种策略和策略组合的最佳对策，即自己的可选策略与其他博弈方每种策略配合，给自己带来最大得益的策略，然后通过对其他博弈方策略选择的判断，预测博弈的可能结果和确定自己的最优策略。
博弈论
Game Theory
Tu qiao ping
2009.3
第二章完全信息静态博弈
2.1 基本分析思路和方法上策均衡严格下策反复消去法划线法箭头法
2.2 纳什均衡纳什均衡的定义纳什均衡与上策均衡和严格下策反复消法
2.3 举例 2.4 混合策略和混合策略纳什均衡

答(1)博弈论,英文为game theory,是研究决策主体的行为发生解析

答：（1）博弈论，英文为“game theory”，是研究决策主体的行为发生直接相互作用时候的决策以及这种决策的均衡问题的，也就是说，当一个主体，好比说一个人或一个企业的选择受到其他人、其他企业选择的影响，而且反过来影响到其他人、其他企业选择时的决策问题和均衡问题。

（2）我国外贸额90%以上是同世贸组织成员发生的，此时的中国就类似于智猪博弈中的“小猪”，世贸组织成员类似于“大猪”，因为一旦发生贸易摩擦，往往以双边政治关系为“抵押”，却无权引用多边争端解决机制，从而在贸易中处于被动地位。

而无权引用乌拉圭回合反倾销协议和反补贴协议下的权益，也使中国往往成为歧视性反倾销反补贴的首要对象。

（3）加入世界贸易组织能够为中国在新世纪的发展中争取更有利的生存环境。

加入世贸组织，也将带来一些压力和挑战，如会给国内的部分企业带来更大的竞争压力。

但专家们指出，这些压力将促使企业加速技术改造，改进管理，提高产品质量，在全球化的经济环境下不断提高自身的竞争能力，进入良性循环状态。

加入WTO组织之后，由于可借助WTO 的仲裁机制，类似针对中国的单方面的制裁将会多了一个申诉的渠道，不会光吃哑巴亏。

就如斗鸡博弈理论一样，其他国家单方面对我国进行歧视性反倾销时，我国可以利用世贸组织的游戏规则行事，避免过于被动。

同时，中国作为世贸组织的正式成员将可直接参与二十一世纪国际贸易规则的决策过程，摆脱别人制定规则，中国被动接受的不利状况，而且参与制定规则，有利于使中国的合法权益得到反映；同时，可把国际贸易争端交到世贸组织的仲裁机关处理，免受不公正处罚。

game-theory1--博弈论-英文

Economic Models - Why?
• models are NOT designed to tell us what people will do, they are not designed to be descriptive
Introduction to Game Theory
Lecture 1
Disclaimer: this presentation is only a supporting material and is not sufficient to master the topics covered during the lecture. Study of relevant books is strongly recommended.
6
Introduction Economic Models Game Theory Models Games Summary
Economic Models - Problem
• based on Homo Rationalis
• acts purposefully and logically • has well-defined goals • has motivation and ability to approach them • does not exist!
• Osborne, M. J. – An Introduction to Game Theory Gibbons, R. – A Primer in Game Theory Suggested articles
• Important information on webpage
• Grading: Midterm 30%, Final 60%, Homework 10%, Experiments up to 5%