The Consistent Preferences Approach to Deductive Reasoning in Games

1. Auflage 2010
ISBN: 978-0-387-26237-6
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 203 Seiten

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.

Autoren/Hrsg.

Inhaltsverzeichnis

1;Table of Contents;7
2;List of Figures;10
3;List of Tables;12
4;Preface;13
4.1;Structure of the book;13
4.2;Notes on the history of t he research program;14
4.3;Acknowledgements;15
5;Copyright Permissions;17
6;Chapter 1 INTRODUCTION;18
6.1;1.1 Conditions for Nash equilibrium;19
6.2;1.2 Modeling backward and forward induction;23
6.3;1.3 Integrating decision theory and game theory;24
7;Chapter 2 MOTIVATING EXAMPLES;28
7.1;2.1 Six examples;28
7.2;2.2 Overview over concepts;34
8;Chapter 3 DECISION-THEORETIC FRAMEWORK;38
8.1;3.1 Motivation;39
8.2;3.2 Axioms;43
8.3;3.3 Representation results;46
9;Chapter 4 BELIEF OPERATORS;54
9.1;4.1 From preferences to accessibility relations;57
9.2;4.2 Defining and characterizing belief operators;61
9.3;4.3 Properties of belief operators;63
9.4;4.4 Relation to other non-monotonic operators;65
10;Chapter 5 BASIC CHARACTERIZATIONS;69
10.1;5.1 Epistemic modeling of strategic games;69
10.2;5.2 Consistency of preferences;74
10.3;5.3 Admissible consistency of preferences;78
11;Chapter 6 RELAXING COMPLETENESS;84
11.1;6.1 Epistemic modeling of strategic games (cont.);84
11.2;6.2 Consistency of preferences (cont.);88
11.3;6.3 Admissible consistency of preferences (cont.);90
12;Chapter 7 BACKWARD INDUCTION;94
12.1;7.1 Epistemic modeling of extensive games;97
12.2;7.2 Initial belief of opponent rationality;102
12.3;7.3 Belief in each subgame of opponent rationality;104
12.4;7.4 Discussion;109
13;Chapter 8 SEQUENTIALITY;113
13.1;8.1 Epistemic modeling of extensive games (cont. );115
13.2;8.2 Sequential consistency;118
13.3;8.3 Weak sequential consistency;121
13.4;8.4 Relation to backward induction;127
14;Chapter 9 QUASI-PERFECTNESS;129
14.1;9.1 Quasi-perfect consistency;130
14.2;9.2 Relating rationalizability concepts;132
15;Chapter 10 PROPERNESS;134
15.1;10.1 An illustration;136
15.2;10.2 Proper consistency;137
15.3;10.3 Relating rationalizability concepts (cont.);140
15.4;10.4 Induction in a betting game;142
16;Chapter 11 CAPTURING FORWARD INDUCTION THROUGH FULL PERMISSIBILITY;146
16.1;11.1 Illustrating the key features;148
16.2;11.2 IECFA and fully permissible sets;151
16.3;11.3 Full admissible consistency;155
16.4;11.4 Investigating examples;162
16.5;11.5 Related literature;165
17;Chapter 12 APPLYING FULL PERMISSIBILITY TO EXTENSIVE GAMES;168
17.1;12.1 Motivation;168
17.2;12.2 Justifying extensive form application;172
17.3;12.3 Backward induction;175
17.4;12.4 Forward induction;181
17.5;12.5 Concluding remarks;186
18;Appendix A Proofs of results in Chapter 4;188
19;Appendix B Proofs of results in Chapters 8-10;193
20;Appendix C Proofs of results in Chapter 11;205
21;References;207
22;Index;213
23;About the Author;215