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Mathematics - Applications | The Consistent Preferences Approach to Deductive Reasoning in Games

The Consistent Preferences Approach to Deductive Reasoning in Games

Asheim, Geir B.

2006, XIX, 203 p.

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During the last decade I have explored the consequences of what I have chosen to call the 'consistent preferences' approach to deductive reasoning in games. To a great extent this work has been done in coop­ eration with my co-authors Martin Dufwenberg, Andres Perea, and Ylva Sovik, and it has lead to a series of journal articles. This book presents the results of this research program. Since the present format permits a more extensive motivation for and presentation of the analysis, it is my hope that the content will be of interest to a wider audience than the corresponding journal articles can reach. In addition to active researcher in the field, it is intended for graduate students and others that wish to study epistemic conditions for equilibrium and rationalizability concepts in game theory. Structure of the book This book consists of twelve chapters. The main interactions between the chapters are illustrated in Table 0.1. As Table 0.1 indicates, the chapters can be organized into four dif­ ferent parts. Chapters 1 and 2 motivate the subsequent analysis by introducing the 'consistent preferences' approach, and by presenting ex­ amples and concepts that are revisited throughout the book. Chapters 3 and 4 present the decision-theoretic framework and the belief operators that are used in later chapters. Chapters 5, 6, 10, and 11 analyze games in the strategic form, while the remaining chapters-Chapters 7, 8, 9, and 12-are concerned with games in the extensive form.

Content Level » Research

Keywords » Asheim - Epistemic Modeling - Equilibrium - Rationalizability - decision theory - game theory - paraplusig

Related subjects » Applications - Economic Theory - Mathematics - Operations Research & Decision Theory

Table of contents 

Dedication v List of Figures xi List of Tables xiii Preface xv 1. INTRODUCTION 1.1 Conditions for Nash equilibrium 1.2 Modeling backward and forward induction 1.3 Integrating decision theory and game theory 2. MOTIVATING EXAMPLES 2.1 Six examples 2.2 Overview over concepts 3. DECISION-THEORETIC FRAMEWORK 3.1 Motivation 3.2 Axioms 3.3 Representation results 4. BELIEF OPERATORS 4.1 From preferences to accessibility relations 4.2 Defining and characterizing belief operators 4.3 Properties of belief operators 4.4 Relation to other non-monotonic operators 5. BASIC CHARACTERIZATIONS 5.1 Epistemic modeling of strategic games 5.2 Consistency of preferences 5.3 Admissible consistency of preferences 6. RELAXING COMPLETENESS 6.1 Epistemic modeling of strategic games (cont.) 6.2 Consistency of preferences (cont.) 6.3 Admissible consistency of preferences (cont.) 7. BACKWARD INDUCTION 7.1 Epistemic modeling of extensive games 7.2 Initial belief of opponent rationality 7.3 Belief in each subgame of opponent rationality 7.4 Discussion 8. SEQUENTIALITY 8.1 Epistemic modeling of extensive games (cont.) 8.2 Sequential consistency 8.3 Weak sequential consistency 8.4 Relation to backward induction 9. QUASI-PERFECTNESS 9.1 Quasi-perfect consistency 9.2 Relating rationalizability concepts 10. PROPERNESS 10.1 An illustration 10.2 Proper consistency 10.3 Relating rationalizability concepts (cont.) 10.4 Induction in a betting game 11. CAPTURING FORWARD INDUCTION THROUGH FULL PERMISSIBILITY 11.1 Illustrating the key features 11.2 IECFA and fully permissible sets 11.3 Full admissible consistency 11.4 Investigating examples 11.5 Related literature 12. APPLYING FULL PERMISSIBILITYTO EXTENSIVE GAMES 12.1 Motivation 12.2 Justifying extensive form application 12.3 Backward induction 12.4 Forward induction 12.5 Concluding remarks Appendices A. Proofs of results in Chapter 4 B. Proofs of results in Chapters 8–10 C. Proofs of results in Chapter 11 References Index

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