Contents
Preface

Introduction
1.1 What is game theory?
An outline ofthe history of game theory
John von Neumann
1.2 The theory of rational choice
1.3 Coming attractions: interacting decision-makers
Notes
I Games with Perfect Information

2 Nash Equilibrium: Theory
2,1 Strategic games
2.2 Example: the Prisoner's Dilemma
2.3 Example: Bach orStravinsky?
2.4 Example: Matching Pennies
2.5 Example: the Stag Hunt
2.6 Nash equilibrium
John F. Nash, Jr.
Studying Nash equilibrium experimentally
2.7 Examples of Nash equilibrium
Experimental evidence on the Prisoner's Dilemma
Focal points
2.8 Best response functions
2.9 Dominated actions
2.10 Equilibrium in a single population: symmetric games and symmetric equilibria
Notes

3 Nash Equilibrium: lllustrations
3.1 Cournot's model ofoligopoly
3.2 Bertrand's model ofoligopoly
Cournot, Bertrand, and Nash: some historical notes
3.3 Electoral competition
3.4 The Warof Attrition
3.5 Auctions
Auctions from Babylonia to eBay
3.6 Accident law
Notes

4 Mixed Strategy Equilibrium
4.1 introduction
Some evidence on expected payoff functions
4.2 Strategic games in which players may randomize
4.3 Mixed strategy Nash equilibrium
4.4 Dominated actions
4.5 Pure equilibria when randomization is allowed
4.6 Illustration: expert diagnosis
4.7 Equilibrium in a single population
4.8 Illustration: reporting a crime
Reporting a crime: social psychology and game theory
4.9 The formation of players' beliefs
4.10 Extension: finding all mixed strategy Nash equilibria
4.11 Extension: games in which each player has a continuum of actions
4.12 Appendix: representing preferences by expected payoffs
Notes

5 Extensive Games with Perfect Information: Theory
5.1 Extensive games with perfect information
5.2 Strategies and outcomes
5.3 Nash equilibrium
5.4 Subgame perfect equilibrium
5.5 Finding subgame perfect equilibria of finite horizon games: backward induction
Ticktacktoe, chess, and related games
Notes

6 Extensive Games with Perfect Information: lllustrations
6.1 The ultimatum game, the hold up game, and agenda control
Experiments on the ultimatum game
6.2 Stackeiberg's model of duopoly
6.3 Buying votes
6.4 A race
Notes

7 Extensive Games with Perfect Information: Extensions and Discussion
7.1 Allowing for simultaneous moves
More experimental evidence on sub game perfect equilibrium
7.2 Ilustration: entry into a monopolized industry
7.3 IIustration: electora competition with strategic voters
7.4 Ilustration: committee decision-making
7.5 Ilustration: exit from a declining industry
7.6 Allowing for exogenous uncertainty
7.7 Discussion: subgame perfect equilibrium and backward induction
Experimental evidence on the centipede game
Notes

8 Coalitional Games and the Core
8.1 Coalitional games
8.2 The core
8.3 Ilustration: ownership and the distribution of wealth
8.4 Ilustration: exchanging homogeneous houses
8.5 Ilustration: exchanging heterogeneous houses
8.6 Ilustration: voting
8.7 Ilustration: matching
Matching doctors with hospitals
8.8 Discussion: other solution concepts
Notes
II Games with Imperfect Information

9 Bayesian Games
9.1 Motivational examples
9.2 General definitions
9.3 Two examples concerning information
9.4 lllustration: Cournot's duopoly game with imperfect information
9.5 lllustration: providing a public good
9.6 lllustration: auctions
Auctions of the radio spectrum
9.7 lllustration: juries
9.8 Appendix: auctions with an arbitrary distribution of valuations
Notes

10 Extensive Games with Imperfect Information
10.1 Extensive games with imperfect information
10.2 Strategies
10.3 Nash equilibrium
10.4 Beliefs and sequential equilibrium
10.5 Signaling games
10.6 lllustration: conspicuous expenditure as a signal of quality
10.7 lllustration: education as a signal of ability
10.8 lllustration: strategic information transmission
10.9 Ilustration: agenda control with imperfect information
Notes
III Variants and Extensions

11 Strictly Competitive Games and Maxminimization
11.1 Maxminimization
11.2 Maxminimization and Nash equilibrium
11.3 Strictly competitive games
11.4 Maxminimization and Nash equilibrium in strictly competitive games
Maxminimization: some history
Empirical tests: experiments, tennis, and soccer
Notes

12 Rationalizability
12.1 Rationalizability
12.2 Iterated elimination of strictly dominated actions
12.3 Iterated elimination of weakly dominated actions
12.4 Dominance solvability
Notes

13 Evolutionary Equilibrium
13.1 Monomorphic pure strategy equilibrium
Evolutionary game theory: some history
13.2 Mixed strategies and polymorphic equilibrium
13.3 Asymmetric contests
Side-blotched lizards
Explaining the outcomes of contests in nature
13.4 Variation on a theme: sibling behavior
13.5 Variation on a theme: the nesting behavior of wasps
13.6 Variation on a theme: the evolution of the sex ratio
Notes

14 Repeated Games: The Prisoner's Dilemma
14.1 The main idea
14.2 Preferences
14.3 Repeated games
14.4 Finitely repeated Prisoner's Dilemma
14.5 Infinitely repeated Prisoner's Dilemma
14.6 Strategies in an infinitely repeated Prisoner's Dilemma
14.7 Some Nash equilibria of an infinitely repeated Prisoner's Dilemma
14.8 Nash equilibrium payoffs of an infinitely repeated Prisoner's Dilemma
Experimental evidence
14.9 Subgame perfect equilibria and the one-deviation property
Axelrod's tournaments
14.10 Some subgame perfect equilibria of an infinitely repeated
Prisoner's Dilemma
Reciprocal altruism among sticklebacks
14.11 Subgame perfect equilibrium payoffs of an infinitely repeated Prisoner's Dilemma
Medieval trade fairs
14.12 Concluding remarks
Notes

15 Repeated Games: General Results
15.1 Nash equilibria of general infinitely repeated games
15.2 Subgame perfect equilibria of general infinitely repeated games
15.3 Finitely repeated games
15.4 Variation on a theme: imperfect observability
Notes

16 Bargaining
16.1 Bargaining as an extensive game
16.2 lllustration: trade in a market
16.3 Nash's axiomatic model
16.4 Relation between strategic and axiomatic models
Notes

17 Appendix: Mathematics
17.1 Numbers
17.2 Sets
17.3 Functions
17.4 Profiles
17.5 Sequences
17.6 Probability
17.7 Proofs
References
Index