Nash Equilibrium in Continuous Games and Mixed Strategies Joseph Harrington
Games, Strategies, and Decision Making
Second Edition ©2015
Making the tools and applications of game theory and strategic reasoning fascinating and easy-to-understand, Games, Strategies, and Decision Making introduces core concepts with a minimum of mathematics in order to give you insights into human behavior
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Making the tools and applications of game theory and strategic reasoning fascinating and easy-to-understand, Games, Strategies, and Decision Making introduces core concepts with a minimum of mathematics in order to give you insights into human behavior
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Table of Contents
PART 1 Constructing A Game
1 Introduction to Strategic Reasoning
1.1 Introduction
1.2 A Sampling of Strategic Situations
1.3 Whetting Your Appetite: The Game of Concentration
1.4 Psychological Profile of a Player
1.5 Playing the Gender Pronoun Game
2. Building a Model of a Strategic Situation
2.1 Introduction
2.2 Extensive Form Games: Perfect Information
2.3 Extensive Form Games: Imperfect Information
2.4 What Is a Strategy?
2.5 Strategic Form Games
2.6 Moving from the Extensive Form and Strategic Form
2.7 Going from the Strategic Form to the Extensive Form
2.8 Common Knowledge
2.9 A Few More Issues in Modeling Games
PART 2 Strategic Form Games
3. Eliminating the Impossible: Solving a Game when Rationality Is Common Knowledge
3.1 Introduction
3.2 Solving a Game when Players Are Rational
3.3 Solving a Game when Players Are Rational and Players Know that Players Are Rational
3.4 Solving a Game when Rationality Is Common Knowledge
3.5 Do people believe that people believe that people are rational?
3.6 Appendix: Strict and Weak Dominance
3.7 Appendix: Rationalizability (Advanced)
3.8 Appendix: Strict Dominance with Randomization
4. Stable Play: Nash Equilibria in Discrete Games with Two or Three Players
4.1 Defining Nash Equilibrium
4.2 Classic Two-Player Games
4.3 The Best-Reply Method
4.4 Three-Player Games
4.5 Foundations of Nash Equilibrium
4.6 Fictitious Play and Convergence to Nash Equilibrium
4.6 Appendix: Formal Definition of Nash Equilibrium
5. Stable Play: Nash Equilibria in Discrete n-Player Games
5.1 Introduction
5.2 Symmetric Games
5.3 Asymmetric Games
5.4 Selecting among Nash Equilibria
6. Stable Play: Nash Equilibria in Continuous Games
6.1 Introduction
6.2 Solving for Nash Equilibria without Calculus
6.3 Solving for Nash Equilibria with Calculus
7. Keep 'Em Guessing: Randomized Strategies
7.1 Police Patrols and the Drug Trade
7.2 Making Decisions under Uncertainty
7.3 Mixed Strategies and Nash Equilibrium
7.4 Examples
7.5 Advanced Examples
7.6 Pessimism and Games of Pure Conflict
7.7 Appendix: Formal Definition of Nash Equilibrium in Mixed Strategies
PART 3 Extensive Form Games
8. Taking Turns: Sequential Games with Perfect Information
8.1 Introduction
8.2 Backward Induction and Subgame Perfect Nash Equilibrium
8.3 Examples
8.4 Waiting Games: Preemption and Attrition
8.5 Do People Reason Using Backward Induction?
9. Taking Turns in the Dark: Sequential Games with Imperfect Information
9.1 Introduction
9.2 Subgame Perfect Nash Equilibrium
9.3 Examples
9.4 Commitment
9.5 Forward Induction
PART 4 Games of Incomplete Information
10. I Know Something You Don't Know: Games with Private Information
10.1 Introduction
10.2 A Game of Incomplete Information: The Munich Agreement
10.3 Bayesian Games and Bayes–Nash Equilibrium
10.4 When All Players Have Private Information: Auctions
10.5 Voting on Committees and Juries
10.6 Appendix: Formal Definition of Bayes–Nash Equilibrium
10.7 Appendix: First-Price, Sealed-Bid Auction with a Continuum of Types
11. What You Do Tells Me Who You Are: Signaling Games
11.1 Introduction
11.2 Perfect Bayes–Nash Equilibrium
11.3 Examples
11.4 Selecting Among Perfect Bayes-Nash Equilibria: The Intuitive Criterion
11.5 Appendix: Bayes's Rule and Updating Beliefs
11.6 Appendix: Formal Definition of Perfect Bayes-Nash Equilibrium for Signaling Games
12. Lies and the Lying Liars That Tell Them: Cheap Talk Games
12.1 Introduction
12.2 Communication in a Game-Theoretic World
12.3 Signaling Information
12.4 Signaling Intentions
PART 5 Repeated Games
13. Playing Forever: Repeated Interaction with Infinitely Lived Players
13.1 Trench Warfare in World War I
13.2 Constructing a Repeated Game
13.3 Trench Warfare: Finite Horizon
13.4 Trench Warfare: Infinite Horizon
13.5 Some Experimental Evidence for the Repeated Prisoners' Dilemma
13.6 Appendix: Present Value of a Payoff Stream
13.7 Appendix: Dynamic Programming
14. Cooperation and Reputation: Applications of Repeated Interaction with Infinitely Lived Player
14.1 Introduction
14.2 A Menu of Punishments
14.3 Quid-Pro-Quo
14.4 Reputation
14.5 Imperfect Monitoring and Antiballistic Missiles
15. Interaction in Infinitely Lived Institutions
15.1 Introductions
15.2 Cooperation with Overlapping Generations
15.3 Cooperation in a Large Population
PART 6 Evolutionary Game Theory
16. Evolutionary Game Theory and Biology: Evolutionarily Stable Strategies
16.1 Introducing Evolutionary Game Theory
16.2 Hawk–Dove Conflict
16.3 Evolutionarily Stable Strategy
16.4 Properties of an ESS
16.5 Multipopulation Games
16.6 Evolution of Spite
17. Evolutionary Game Theory and Biology: Replicator Dynamics
17.1 Introduction
17.2 Replicator Dynamics and the Hawk–Dove Game
17.3 General Definition of the Replicator Dynamic
17.4 ESS and Attractors of the Replicator Dynamic
17.5 Examples
Solutions to "Check Your Understanding" Questions
Glossary
Index
Joseph E. Harrington, Jr.
Joseph E. Harrington, Jr. is Professor of Economics at Johns Hopkins University. He has served on numerous editorial boards, including the RAND Journal of Economics, Foundations and Trends in Microeconomics, and the Southern Economic Journal. His research has appeared in top journals in a variety of disciplines including economics (e.g., the American Economic Review, Journal of Political Economy, and Games and Economic Behavior), political science (Economics and Politics, Public Choice), sociology (American Journal of Sociology), organizational behavior (Management Science), and psychology (Journal of Mathematical Psychology). He is a co-author of the leading textbook Economics of Regulation and Antitrust, which is currently in its fourth edition.
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