Book on Epistemic Game Theory

Background

In January 2007 I started working on a textbook called “Epistemic Game Theory: Reasoning and Choice”. The book has been published in June 2012 by Cambridge University Press. This book is a non-technical introduction into the world of epistemic game theory. The book is very much suited for class room use. It can be used, for instance, for a course in game theory to third-year bachelor students, master students and PhD students. Researchers can also use the book as an introduction to the field.

The purpose of this book is to introduce the reader, in an intuitive and unified way, to some of the main ideas and concepts in Epistemic Game Theory. Every chapter is dedicated to one idea, which typically represents a particular way of reasoning about the opponents, and starts by discussing one or more examples that illustrate the idea. It then shows how this idea can be expressed formally within a model, eventually resulting in a formal concept. The next step is to investigate its behavioral consequences, that is, if you use this particular way of reasoning, then what choices can you plausibly make? And is there an algorithm that helps us find those choices? Every chapter is full of examples, usually from “everyday life”, that illustrate each of the aforementioned steps. At the end of every chapter there is a list of practical problems that will train the reader in applying the various ideas, models, concepts and algorithms to concrete game theoretic situations. To all chapters there is also a list of theoretical problems, which should deepen and extend the reader’s knowledge of the various concepts.

Throughout the book I take a one-person perspective, that is, I will always analyze the situations from the perspective of one single person, who reasons about his opponents. More precisely, this means that I restrict attention to the reasoning process of one single person, and investigate how this particular person would act by adapting this way of reasoning about his opponents. This approach is new, but allows me to offer a clean presentation of ideas.

Courses based on the book

Since 2007 I have been giving mini-courses on epistemic game theory at universities across Europe. These mini-courses have been very important for the development of the book: often I have used ideas and examples from that mini-course for my book, but conversely I have also intensively used new chapters of the book for the mini-course.

From 2010 until 2013 I have been giving a seven-week course on epistemic game theory at Maastricht University, for master students, PhD students and researchers. Until 2012 I gave this course together with my friend and colleague Christian Bach. The book has also benefited a lot from that seven-week course. From the seven-week course in 2013 there are video-recordings that you can watch.

Since 2014 we give our EPICENTER Spring Course in Epistemic Game Theory once a year -- a two week intensive course for students all over the world. This course is given by members of our EPICENTER, and the content of that course is very much based on the seven week course I gave until 2013.

If you have any comments on the book, please send me an E-mail at: a.perea@maastrichtuniversity.nl

Contents of the book “Epistemic Game Theory: Reasoning and Choice”

Chapter 1: Introduction

Part I : Standard Beliefs in Static Games

Chapter 2: Belief in the Opponent’s Rationality

2.1. Beliefs about the opponent’s choice 2.2. Utility functions 2.3. More than two players 2.4. Choosing rationally 2.5. Strictly dominated choices

2.6. Belief in the opponents’ rationality 2.7. Graphical method 2.8. Algorithm 2.9. Proofs

Practical problems

Theoretical problems

Literature

Chapter 3: Common Belief in Rationality

3.1. Beliefs about the opponent’s beliefs 3.2. Belief hierarchies 3.3. Epistemic model 3.4. Common belief in rationality 3.5. Graphical method

3.6. Existence 3.7. Algorithm 3.8. Order independence 3.9. Proofs

Practical problems

Theoretical problems

Literature

Chapter 4: Simple Belief Hierarchies

4.1. Simple belief hierarchies 4.2. Nash equilibrium 4.3. Computational method 4.4. Belief that opponents hold correct beliefs 4.5. Proofs

Practical problems

Theoretical problems

Literature

Part II : Lexicographic Beliefs in Static Games

Chapter 5: Primary Belief in the Opponent’s Rationality

5.1. Cautious reasoning about the opponent 5.2. Lexicographic beliefs 5.3. Belief hierarchies and types 5.4. Cautious types 5.5. Primary belief in the opponent’s rationality 5.6. Common full belief in “primary belief in rationality” 5.7 Existence 5.8. Weakly dominated choices 5.9. Algorithm

5.10. Proofs

Practical problems

Theoretical problems

Literature

Chapter 6: Respecting the Opponent’s Preferences

6.1. Respecting the opponent’s preferences 6.2. Common full belief in “respect of preferences” 6.3. Existence 6.4. Why elimination of choices does not work 6.5. Preference restrictions and likelihood orderings 6.6. Algorithm 6.7. Order independence 6.8. Proofs

Practical problems

Theoretical problems

Literature

Chapter 7: Assuming the Opponent’s Rationality

7.1. Assuming the opponent’s rationality 7.2. Common assumption of rationality 7.3. Algorithm 7.4. Order dependence 7.5. Proofs

Practical problems

Theoretical problems

Literature

Part III : Conditional Beliefs in Dynamic Games

Chapter 8: Belief in the Opponents’ Future Rationality

8.1. Belief revision 8.2. Dynamic games 8.3. Conditional beliefs 8.4. Epistemic model 8.5. Belief in the opponents’ future rationality 8.6. Common belief in future rationality 8.7. Existence 8.8. Algorithm 8.9. Order independence 8.10. Backwards order of elimination 8.11. Backward induction

8.12. Games with unobserved past choices 8.13. Bayesian updating 8.14. Proofs

Practical problems

Theoretical problems

Literature

Chapter 9: Strong Belief in the Opponents’ Rationality

9.1. Strong belief in the opponents’ rationality 9.2. Common strong belief in rationality 9.3. Algorithm 9.4. Comparison with backward dominance procedure 9.5. Order dependence 9.6. Rationality orderings 9.7. Bayesian updating 9.8. Proofs

Practical problems

Theoretical problems

Literature

Bibliography

Index