Consistent Preferences Approach to Deductive Reasoning in Games (eBook)

Geir B. Asheim (Autor)

eBook Download: PDF

2010 | 2006
XIX, 203 Seiten
Springer US (Verlag)
978-0-387-26237-6 (ISBN)

Infos

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.

Geir B. Asheim is Professor of Economics at the University of Oslo,

Norway. In additional to investigating epistemic conditions for gametheoretic

solution concepts, he is doing research on questions relating to

intergenerational justice.

Inhalt

Table of Contents 7
List of Figures 10
List of Tables 12
Preface 13
Structure of the book 13
Notes on the history of t he research program 14
Acknowledgements 15
Copyright Permissions 17
Chapter 1 INTRODUCTION 18
1.1 Conditions for Nash equilibrium 19
1.2 Modeling backward and forward induction 23
1.3 Integrating decision theory and game theory 24
Chapter 2 MOTIVATING EXAMPLES 28
2.1 Six examples 28
2.2 Overview over concepts 34
Chapter 3 DECISION-THEORETIC FRAMEWORK 38
3.1 Motivation 39
3.2 Axioms 43
3.3 Representation results 46
Chapter 4 BELIEF OPERATORS 54
4.1 From preferences to accessibility relations 57
4.2 Defining and characterizing belief operators 61
4.3 Properties of belief operators 63
4.4 Relation to other non-monotonic operators 65
Chapter 5 BASIC CHARACTERIZATIONS 69
5.1 Epistemic modeling of strategic games 69
5.2 Consistency of preferences 74
5.3 Admissible consistency of preferences 78
Chapter 6 RELAXING COMPLETENESS 84
6.1 Epistemic modeling of strategic games (cont.) 84
6.2 Consistency of preferences (cont.) 88
6.3 Admissible consistency of preferences (cont.) 90
Chapter 7 BACKWARD INDUCTION 94
7.1 Epistemic modeling of extensive games 97
7.2 Initial belief of opponent rationality 102
7.3 Belief in each subgame of opponent rationality 104
7.4 Discussion 109
Chapter 8 SEQUENTIALITY 113
8.1 Epistemic modeling of extensive games (cont. ) 115
8.2 Sequential consistency 118
8.3 Weak sequential consistency 121
8.4 Relation to backward induction 127
Chapter 9 QUASI-PERFECTNESS 129
9.1 Quasi-perfect consistency 130
9.2 Relating rationalizability concepts 132
Chapter 10 PROPERNESS 134
10.1 An illustration 136
10.2 Proper consistency 137
10.3 Relating rationalizability concepts (cont.) 140
10.4 Induction in a betting game 142
Chapter 11 CAPTURING FORWARD INDUCTION THROUGH FULL PERMISSIBILITY 146
11.1 Illustrating the key features 148
11.2 IECFA and fully permissible sets 151
11.3 Full admissible consistency 155
11.4 Investigating examples 162
11.5 Related literature 165
Chapter 12 APPLYING FULL PERMISSIBILITY TO EXTENSIVE GAMES 168
12.1 Motivation 168
12.2 Justifying extensive form application 172
12.3 Backward induction 175
12.4 Forward induction 181
12.5 Concluding remarks 186
Appendix A Proofs of results in Chapter 4 188
Appendix B Proofs of results in Chapters 8-10 193
Appendix C Proofs of results in Chapter 11 205
References 207
Index 213
About the Author 215

Produkt-Details

• Erscheint lt. Verlag: 7.7.2010
• Reihe/Serie: Theory and Decision Library C
• Reihe/Serie: Theory and Decision Library C
• Zusatzinfo: XIX, 203 p.
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik
• Themenwelt: Wirtschaft ► Allgemeines / Lexika
• Themenwelt: Wirtschaft ► Betriebswirtschaft / Management ► Planung / Organisation
• Themenwelt: Wirtschaft ► Betriebswirtschaft / Management ► Unternehmensführung / Management
• Themenwelt: Wirtschaft ► Volkswirtschaftslehre
• Schlagworte: Asheim • Decision Theory • Epistemic Modeling • Equilibrium • Game Theory • Paraplusig • Rationalizability
• ISBN-10: 0-387-26237-7 / 0387262377
• ISBN-13: 978-0-387-26237-6 / 9780387262376