Epistemic Game Theory: Reasoning and Choice

Book
Author/s:
Andrés Perea
Publisher:
Cambridge University Press
Year:
2012
In everyday life we must often reach decisions while knowing that the outcome will not only depend on our own choice, but also on the choices of others. These situations are the focus of epistemic game theory. Unlike classical game theory, it explores how people may reason about their opponents before they make their final choice in a game. Packed with examples and practical problems based on stories from everyday life, this is the first textbook to explain the principles of epistemic game theory. Each chapter is dedicated to one particular, natural way of reasoning. The book then shows how each of these ways of reasoning will affect the final choices that can rationally be made and how these choices can be found by iterative procedures. Moreover, it does so in a way that uses elementary mathematics and does not presuppose any previous knowledge of game theory.

Contents

hapter 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

Developed by Paolo Gittoi