A Primer in Game Theory

TL;DR: Static games of complete information dynamic games ofcomplete information static games of incomplete information staticGames of incomplete Information dynamic gamesof incomplete information.

Abstract: PrefaceGame theory is the study of multiperson decision problems. Such 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 applications of game theory arise in fields of economics other than industrial organization. At the micro level, models of trading processes (such as bargaining and auction models) involve game theory. At an intermediate level of aggregation, labor and financial 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 are multiperson problems within a firm: many workers may vie for one promotion; several divisions may compete for the corporation's investment capital. Finally, at a high level of aggregation, international economics includes models in which countries compete (or collude) in choosing tariffs and other 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 models 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 appear but play a lesser role. Second, the applications illustrate the process of model building -- the process of translating an informal description of a multiperson decision situation into a formal, game-theoretic problem to be analyzed. Third, the variety of applications shows that similar issues arise in different areas of economics, and that the same game-theoretic tools can be applied in each setting. In order to emphasize the broad potential scope of the theory, conventional applications from industrial organization largely have been replaced by applications from labor, macro, and other applied fields in economics.We will discuss four classes of games: static games of complete information, dynamic games of complete information, static games of incomplete information, and dynamic games of incomplete information. (A game has incomplete information if one player does not know another player's payoff, such as in an auction when one bidder does not know how much another bidder is willing to pay for the good being sold.) Corresponding to these four classes of games will be four notions of equilibrium in games: Nash equilibrium, subgame-perfect Nash equilibrium, Bayesian Nash equilibrium, and perfect Bayesian equilibrium.Two (related) ways to organize one's thinking about these equilibrium concepts are as follows. First, one could construct sequences of equilibrium concepts of increasing strength, where stronger (i.e., more restrictive) concepts are attempts to eliminate 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 equilibrium in turn is stronger than subgame-perfect Nash equilibrium. Second, one could say that the equilibrium concept of interest 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 perfect) information, and equivalent to Bayesian Nash equilibrium in static games of incomplete information.The book can be used in two ways. For first-year graduate students in economics, many of the applications will already be familiar, so the game theory can be covered in a half-semester course, leaving many of the applications 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 calculus; the rudiments of probability and analysis are introduced as needed.I learned game theory from David Kreps, John Roberts, and Bob Wilson in graduate school, and from Adam Brandenburger, Drew Fudenberg, and Jean Tirole afterward. I owe the theoretical perspective in this book to them. The focus on applications and other aspects of the pedagogical style, however, are largely due to the students in the MIT Economics Department from 1985 to 1990, who inspired and rewarded the courses that led to this book. I am very grateful for the insights and encouragement all these friends have provided, as well as for the many helpful comments on the manuscript I received from Joe Farrell, Milt Harris, George Mailath, Matthew Rabin, Andy Weiss, and several anonymous reviewers. Finally, I am glad to acknowledge the advice and encouragement of Jack Repcheck of Princeton University Press and financial support from an Olin Fellowship in Economics at the National Bureau of Economic Research.