A Primer in Game Theory.docx

1、A Primer in Game TheoryA Primer in Game TheoryA Primer in Game Theory Robert Gibbons Contents Prefacexj 1 Static Games of Complete Information 11.1 Basic Theory: Normal-Form Games and Nash Equilibrium21.1. A Normal-Form Representation of Games . . 2 1.1.8B Iterated Elimination of Strictly Dominated

2、Strategies41.1 .C Motivation and Definition of Nash Equilibrium 8 1.2 Applications141.2. A Cournot Model of Duopoly141.2.B Bertrand Model of Duopoly 21 1.2.C Final-Offer Arbitration221.2.D The Problem of the Commons271.3 Advanced Theory: Mixed Strategies and Existence of Equilibrium29 1.3.A Mixed St

3、rategies291.3.B Existence of Nash Equilibrium 331.4 Further Reading481.5 Problems481.6 References512 Dynamic Games of Complete Information 55 2.1 Dynamic Games of Complete and Perfect Information572.1.A Theory: Backwards Induction57 2.1.B Stackelberg Model of Duopoly 612.1.C Wages and Employment in

4、a Unionized Firm 64 2.1.D Sequential Bargaining682.2 Two-Stage Games of Complete but Imperfect Informationvn Contents be 12.A ;Theory: Subgame Perfection 71 4.2.B job-Market Signaling 190IB4.2.C Corporate Investment and Capital Structure . 205 Bank Runs73- C Tariffs and Imperfect Internationa4.2.D M

5、onetary Policy208l Competition754.3 Other Applications of Perfect Bayesian 2.2.D Tournaments79Equilibrium. 210 2.3 Repeated Games824.3.A Cheap-Talk Games210;A Theory: Two-Stage Repeated Games 82 4.3.B Sequential Bargaining under Asymmetric 2.3.B Theory: Infinitely Repeated Games88Information218:.C C

6、ollusion between Coumot Duopolists . . . .102 4.3.C Reputation in the Finitely Repeated 23-D Efficiency Wages107Prisoners Dilemma224 E Time-Consistent Monetary Policy 112 4.4 Refinements of Perfect Bayesian Equilibrium 233 2.4 Dynamic Games of Complete but 4.5 Further Reading244Imperfect Information

7、1154.6 Problems245- ;.A Extensive-Form Representation of Games . .115 4.7 References2532.4.B Subgame-Perfect Nash Equilibrium1222.5 Further Reading129Index 77 16 Problems13017 References138Static Games of Incomplete Information 143 3.1 Theory: Static Bayesian Games and Bayesian Nash Equilibrium1443.

8、1.A An Example: Cournot Competition under Asymmetric Information144 3.1.B Normal-Form Representation of Static Bayesian Games1463.1.C Definition of Bayesian Nash Equilibrium . . . 149 31 Applications1523.2.A Mixed Strategies Revisited1523.2.B An Auction1553.2.C A Double Auction158 3.3 The Revelation

9、 Principle1643.4 Further Reading1683.5 Problems1693.6 References1721 Dynamic Games of Incomplete Information 173 Introduction to Perfect Bayesian Equilibrium 175Signaling Games183Perfect Bayesian Equilibrium in Signaling Games183Preface Game theory is the study of multiperson decision problems. Such

10、 problems arise frequently in economics. As is widely appreciated, for example, oligopolies present multiperson problems each firm must consider what the others will do. But many other ap?plications of game theory arise in fields of economics other than industrial organization. At the micro level, m

11、odels of trading processes (such as bargaining and auction models) involve game theory. At an intermediate level of aggregation, labor and finan?cial economics include game-theoretic models of the behavior of a firm in its input markets (rather than its output market, as in an oligopoly). There also

12、 are multiperson problems within a firm: many workers may vie for one promotion; several divisions may compete for the corporations investment capital. Finally, at a high level of aggregation, international economics includes models in which countries compete (or collude) in choosing tariffs and oth

13、er trade policies, and macroeconomics includes models in which the monetary authority and wage or price setters interact strategically to determine the effects of monetary policy. This book is designed to introduce game theory to those who will later construct (or at least consume) game-theoretic mo

14、dels in applied fields within economics. The exposition emphasizes the economic applications of the theory at least as much as the pure theory itself, for three reasons. First, the applications help teach the theory; formal arguments about abstract games also ap?pear but play a lesser role. Second,

15、the applications illustrate the process of model building the process of translating an infor?mal description of a multiperson decision situation into a formal, game-theoretic problem to be analyzed. Third, the variety of ap?plications shows that similar issues arise in different areas of eco?nomics

16、, and that the same game-theoretic tools can be applied in XI Preface vixm i I learned game theory from David Kreps, John Roberts, and each setting. In order to emphasize the broad potential scope of Bob Wilson in graduate school, and from Adam Brandenburger, tiie theory, conventional applications f

17、rom industrial organization Drew Fudenberg, and Jean Tirole afterward. I owe the theoreti?largely have been replaced by applications from labor, macro, and other applied fields in economics.1 cal perspective in this book to them. The focus on applications Wand other aspects of the pedagogical style,

18、 however, are largely e will discuss four classes of games: static games of 5com?plete information, dynamic games of complete informationdue to the students in the MIT Economics Department from 1985 , static gameto 1990, who inspired and rewarded the courses that led to this s of incomplete informat

19、ion, and dynamic games of incom?plete information. (A game has incompletebook. I am very grateful for the insights and encouragement all information if one player does not know another playersthese friends have provided, as well as for the many helpful com? payoff, such as in an auc?tion when one bi

20、dder does not knowments on the manuscript I received from Joe Farrell, Milt Harris, how much another bidder is willing to pay for the good being sold.) Corresponding to these George Mailath, Matthew Rabin, Andy Weiss, and several anony?four classes of games will be four notions of equilibrium in gam

21、es: mous reviewers. Finally, I am glad to acknowledge the advice and Nash equilibrium, subgame-perfect Nash equilibrium, Bayesian encouragement of Jack Repcheck of Princeton University Press and Nash equilibrium, and perfect Bayesian equilibrium. financial support from an Olin Fellowship in Economic

22、s at the Na?Twotional Bureau of Economic Research. (related) ways to organize ones thinking about these equi?librium concepts are as follows. First, one could construct se?quences of equilibrium concepts of increasing strength, where stronger (i.e., more restrictive) concepts are attempts to elimina

23、te implausible equilibria allowed by weaker notions of equilibrium. We will see, for example, that subgame-perfect Nash equilibrium is stronger than Nash equilibrium and that perfect Bayesian equi?librium in turn is stronger than subgame-perfect Nash equilib?rium. Second, one could say that the equi

24、librium concept of in?terest is always perfect Bayesian equilibrium (or perhaps an even stronger equilibrium concept), but that it is equivalent to Nash equilibrium in static games of complete information, equivalent to subgame-perfection in dynamic games of complete (and per?fect) information, and

25、equivalent to Bayesian Nash equilibrium in static games of incomplete information. The book can be used in two ways. For first-year graduate stu?dents in economics, many of the applications will already be famil?iar, so the game theory can be covered in a half-semester course, leaving many of the ap

26、plications to be studied outside of class. For undergraduates, a full-semester course can present the theory a bit more slowly, as well as cover virtually all the applications in class. The main mathematical prerequisite is single-variable cal?culus; the rudiments of probability and analysis are int

27、roduced as needed. A good source for applications oi game theory in industrial organization is MiesTheTheon/offnctusfrialOrganizaiion (MIT Press, 1988). Chapter 1 Static Games of Complete Information In this chapter we consider games of the following simple form: first the players simultaneously cho

28、ose actions; then the players receive payoffs that depend on the combination of actions just cho?sen. Within the class of such static (or simultaneous-move) games, we restrict attention to games of complete information. That is, each players payoff function (the function that determines the players

29、payoff from the combination of actions chosen by the players) is common knowledge among all the players. We consider dynamic (or sequential-move) games in Chapters 2 and 4, and games of incomplete information (games in which some player is uncertain about another players payoff function as in an auc

30、tion where each bidders willingness to pay for the good being sold is un?known to the other bidders) in Chapters 3 and 4. In Section 1.1 we take a first pass at the two basic issues in game theory: how to describe a game and how to solve the re?sulting game-theoretic problem. We develop the tools we

31、 will use in analyzing static games of complete information, and also the foundations of the theory we will use to analyze richer games in later chapters. We define the normal-form representation of a game and the notion of a strictly dominated strategy. We show that some games can be solved by appl

32、ying the idea that rational players do not play strictly dominated strategies, but also that in other games this approach produces a very imprecise prediction about the play of the game (sometimes as imprecise as ;anything could 1 2 STATIC GAMES OF COMPLETE INFORMATION D/ip?r Tlionni 3 happen;). We then motivate and define Nash equilibrium a so?lution concept that produces much tighter predictionseparate cells and explain the consequences that will follow from s in a very broadthe actions they could take. If neit