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This book introduces one of the most powerful tools of modern economics to a wide audience: those who will later construct or consume game-theoretic models. Robert Gibbons addresses scholars in applied fields within economics who want a serious and thorough discussion of game theory but who may have found other works overly abstract. Gibbons emphasizes the economic applications of the theory at least as much as the pure theory itself; formal arguments about abstract games play a minor role. The applications illustrate the process of model building--of translating an informal description of a multi-person decision situation into a formal game-theoretic problem to be analyzed. Also, 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 have been largely replaced by applications from labor, macro, and other applied fields in economics. The book covers four classes of games, and four corresponding notions of equilibrium: static games of complete information and Nash equilibrium, dynamic games of complete information and subgame-perfect Nash equilibrium, static games of incomplete information and Bayesian Nash equilibrium, and dynamic games of incomplete information and perfect Bayesian equilibrium.
1
Static Games of Complete Information
1
1.1
Basic Theory: Narmal-Form Games and Nash Equilibrium
2
1.1.A
Normal-Form Representation of Games
2
1.1.B
Iterated Elimination of Strictly Dominated Strategies
4
1.1.C
Motivation and Definition of Nash Equilibriuin
8
1.2
Applications
14
1.2.A
Cournot Model of Duopoly
14
1.2.B
Bertrand Model of Duopoly
21
1.2.C
Final-Offer Arbitration
22
1.2.D
The Problem of the Commons
27
1.3
Advanced Theory: Mixed Strategies and Existence of Equilibriutn
29
1.3.A
Mixed Strategies
29
1.3.B
Existence of Nash Equilibrium
33
2
Dynamic Games of Complete Information
55
2.1
Dynamic Games of Complete and Perfect Information
57
2.1.A
Theory: Backwards Induction
57
2.1.B
Stackelberg Model of Duopoly
61
2.1.C
Wages and Employment in a Unionized Firm
64
2.1.D
Sequential Bargaining
68
2.2
Two-Stage Games of Complete but Imperfect Information
71
2.2.A
Theory: Subgame Perfection
71
2.2.B
Bank Runs
73
2.2.C
Tariffs and Imperfect International Competition
75
2.2.D
Tournaments
79
2.3
Repeated Games
82
2.3.A
Theory: Two-Stage Repeated Games
82
2.3.B
Theory: Infinitely Repeated Games
88
2.3.C
Collusion between Cournot Duopolists
102
2.3.D
Efficiency Wages
107
2.3.E
Time-Consistent Monetary Policy
112
2.4
Dynamic Games of Complete but Imperfect Information
115
2.4.A
Extensive-Form Representation of Games
115
2.4.B
Subgame-Perfect Nash Equilibriuin
122
3
Static Games of Incomplete Information
143
3.1
Theory: Static Bayesian Ganies and Bayesian Nash Equilibrium
144
3.1.A
An Example: Cournot Competition under Asymmetric Information
144
3.1.B
Normal-Form Representation of Static Bayesian Games
146
3.1.C
Definition of Bayesian Nash Equilibrium
149
3.2
Applications
152
3.2.A
Mixed Strategies Revisited
152
3.2.B
An Auction
155
3.2.C
A Double Auction
158
3.3
The Revelation Principle
164
4
Dynamic Games of Incomplete Information
173
4.1
Introduction to Perfect Bayesian Equilibrium
175
4.2
Signaling Games
183
4.2.A
Perfect Bayesian Equilibrium in Signaling Games
183
4.2.B
Job-Market Signaling
190
4.2.C
Corporate Investment and Capital Structure
205
4.2.D
Monetary Policy
208
4.3
Other Applications of Perfect Bayesian Equilibrium
210
4.3.A
Cheap-Talk Games
210
4.3.B
Sequential Bargaining under Asymmetric Information
218
4.3.C
Reputation in the Finitely Repeated Prisoners' Dilemnia
224
4.4
Refinements of Perfect Bayesian Equilibrium
233
Index
257
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.
Overview
This book introduces one of the most powerful tools of modern economics to a wide audience: those who will later construct or consume game-theoretic models. Robert Gibbons addresses scholars in applied fields within economics who want a serious and thorough discussion of game theory but who may have found other works overly abstract. Gibbons emphasizes the economic applications of the theory at least as much as the pure theory itself; formal arguments about abstract games play a minor role. The applications ...