Consistent preferences approach to deductive reasoning in games:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
New York
Springer
2006
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIX, 202 S. |
| ISBN: | 0387262350 |
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| adam_text | Contents
Dedication v
List of Figures xi
List of Tables xiii
Preface xv
Copyright Permissions xix
1. INTRODUCTION 1
1.1 Conditions for Nash equilibrium 2
1.2 Modeling backward and forward induction 6
1.3 Integrating decision theory and game theory 7
2. MOTIVATING EXAMPLES 11
2.1 Six examples 11
2.2 Overview over concepts 17
3. DECISION-THEORETIC FRAMEWORK 21
3.1 Motivation 22
3.2 Axioms 26
3.3 Representation results 29
4. BELIEF OPERATORS 37
4.1 From preferences to accessibility relations 40
4.2 Defining and characterizing belief operators 44
4.3 Properties of belief operators 46
4.4 Relation to other non-monotonic operators 48
5. BASIC CHARACTERIZATIONS 53
5.1 Epistemic modeling of strategic games 53
5.2 Consistency of preferences 58
viii CONSISTENT PREFERENCES
5.3 Admissible consistency of preferences 62
6. RELAXING COMPLETENESS 69
6.1 Epistemic modeling of strategic games (cont.) 69
6.2 Consistency of preferences (cont.) 73
6.3 Admissible consistency of preferences (cont.) 75
7. BACKWARD INDUCTION 79
7.1 Epistemic modeling of extensive games 82
7.2 Initial belief of opponent rationality 87
7.3 Belief in each subgame of opponent rationality 89
7.4 Discussion 94
8. SEQUENTIALLY 99
8.1 Epistemic modeling of extensive games (cont.) 101
8.2 Sequential consistency 104
8.3 Weak sequential consistency 107
8.4 Relation to backward induction 113
9. QUASI-PERFECTNESS 115
9.1 Quasi-perfect consistency 116
9.2 Relating rationalizability concepts 118
10. PROPERNESS 121
10.1 An illustration 123
10.2 Proper consistency 124
10.3 Relating rationalizability concepts (cont.) 127
10.4 Induction in a betting game 129
11. CAPTURING FORWARD INDUCTION
THROUGH FULL PERMISSIBILITY 133
11.1 Illustrating the key features 135
11.2 IECFA and fully permissible sets 138
11.3 Full admissible consistency 142
11.4 Investigating examples 149
11.5 Related literature 152
Contents ix
12. APPLYING FULL PERMISSIBILITY
TO EXTENSIVE GAMES 155
12.1 Motivation 155
12.2 Justifying extensive form application 159
12.3 Backward induction 162
12.4 Forward induction 168
12.5 Concluding remarks 173
Appendices 175
A Proofs of results in Chapter 4 175
B Proofs of results in Chapters 8-10 181
C Proofs of results in Chapter 11 193
References 195
Index 201
About the author 203
List of Figures
2.1 Gi ( battle-of-the-sexes ). 12
2.2 G2, illustrating deductive reasoning. 13
2.3 G3, illustrating weak dominance. 13
2.4 G3 and a corresponding extensive form T 3 (a cen-
tipede game). 14
2.5 G 2 and a corresponding extensive form T 2. 16
2.6 G i and a corresponding extensive form F j ( battle-
of-the-sexes with an outside option ). 17
3.1 F4 and its strategic form. 25
4.1 The basic structure of the analysis in Chapter 4. 39
7.1 Fs (a four-legged centipede game). 93
8.1 Fg and its strategic form. 112
8.2 Fg and its pure strategy reduced strategic form. 112
10.1 G7, illustrating common certain belief of proper
consistency. 123
10.2 A betting game. 129
10.3 The strategic form of the betting game. 130
11.1 G8, illustrating that IEWDS may be problematic. 134
11.2 G9, illustrating the key features of full admissible
consistency. 136
11.3 G10, illustrating the relation between IECFA and
IEWDS. 142
12.1 Fn and its pure strategy reduced strategic form. 156
xii CONSISTENT PREFERENCES
12.2 Reduced form of F12 (a 3-period prisoners dilemma
game). 166
12.3 C13 (the pure strategy reduced strategic form of
burning money ). 169
12.4 F / and its pure strategy reduced strategic form. 171
12.5 Fi4 and its pure strategy reduced strategic form. 172
List of Tables
0.1 The main interactions between the chapters. xvi
2.1 Relationships between different equilibrium concepts. 18
2.2 Relationships between different rationalizability concepts. 19
3.1 Relationships between different sets of axioms and
their representations. 29
7.1 An epistemic model for G 3 with corresponding ex-
tensive form T 3. 89
7.2 An epistemic model for IV 93
10.1 An epistemic model for the betting game. 131
12.1 Applying IECFA to burning money . 170
|
| adam_txt |
Contents
Dedication v
List of Figures xi
List of Tables xiii
Preface xv
Copyright Permissions xix
1. INTRODUCTION 1
1.1 Conditions for Nash equilibrium 2
1.2 Modeling backward and forward induction 6
1.3 Integrating decision theory and game theory 7
2. MOTIVATING EXAMPLES 11
2.1 Six examples 11
2.2 Overview over concepts 17
3. DECISION-THEORETIC FRAMEWORK 21
3.1 Motivation 22
3.2 Axioms 26
3.3 Representation results 29
4. BELIEF OPERATORS 37
4.1 From preferences to accessibility relations 40
4.2 Defining and characterizing belief operators 44
4.3 Properties of belief operators 46
4.4 Relation to other non-monotonic operators 48
5. BASIC CHARACTERIZATIONS 53
5.1 Epistemic modeling of strategic games 53
5.2 Consistency of preferences 58
viii CONSISTENT PREFERENCES
5.3 Admissible consistency of preferences 62
6. RELAXING COMPLETENESS 69
6.1 Epistemic modeling of strategic games (cont.) 69
6.2 Consistency of preferences (cont.) 73
6.3 Admissible consistency of preferences (cont.) 75
7. BACKWARD INDUCTION 79
7.1 Epistemic modeling of extensive games 82
7.2 Initial belief of opponent rationality 87
7.3 Belief in each subgame of opponent rationality 89
7.4 Discussion 94
8. SEQUENTIALLY 99
8.1 Epistemic modeling of extensive games (cont.) 101
8.2 Sequential consistency 104
8.3 Weak sequential consistency 107
8.4 Relation to backward induction 113
9. QUASI-PERFECTNESS 115
9.1 Quasi-perfect consistency 116
9.2 Relating rationalizability concepts 118
10. PROPERNESS 121
10.1 An illustration 123
10.2 Proper consistency 124
10.3 Relating rationalizability concepts (cont.) 127
10.4 Induction in a betting game 129
11. CAPTURING FORWARD INDUCTION
THROUGH FULL PERMISSIBILITY 133
11.1 Illustrating the key features 135
11.2 IECFA and fully permissible sets 138
11.3 Full admissible consistency 142
11.4 Investigating examples 149
11.5 Related literature 152
Contents ix
12. APPLYING FULL PERMISSIBILITY
TO EXTENSIVE GAMES 155
12.1 Motivation 155
12.2 Justifying extensive form application 159
12.3 Backward induction 162
12.4 Forward induction 168
12.5 Concluding remarks 173
Appendices 175
A Proofs of results in Chapter 4 175
B Proofs of results in Chapters 8-10 181
C Proofs of results in Chapter 11 193
References 195
Index 201
About the author 203
List of Figures
2.1 Gi ("battle-of-the-sexes"). 12
2.2 G2, illustrating deductive reasoning. 13
2.3 G3, illustrating weak dominance. 13
2.4 G3 and a corresponding extensive form T'3 (a "cen-
tipede" game). 14
2.5 G'2 and a corresponding extensive form T'2. 16
2.6 G'i and a corresponding extensive form F'j ("battle-
of-the-sexes with an outside option"). 17
3.1 F4 and its strategic form. 25
4.1 The basic structure of the analysis in Chapter 4. 39
7.1 Fs (a four-legged "centipede" game). 93
8.1 Fg and its strategic form. 112
8.2 Fg and its pure strategy reduced strategic form. 112
10.1 G7, illustrating common certain belief of proper
consistency. 123
10.2 A betting game. 129
10.3 The strategic form of the betting game. 130
11.1 G8, illustrating that IEWDS may be problematic. 134
11.2 G9, illustrating the key features of full admissible
consistency. 136
11.3 G10, illustrating the relation between IECFA and
IEWDS. 142
12.1 Fn and its pure strategy reduced strategic form. 156
xii CONSISTENT PREFERENCES
12.2 Reduced form of F12 (a 3-period "prisoners' dilemma"
game). 166
12.3 C13 (the pure strategy reduced strategic form of
"burning money"). 169
12.4 F'/ and its pure strategy reduced strategic form. 171
12.5 Fi4 and its pure strategy reduced strategic form. 172
List of Tables
0.1 The main interactions between the chapters. xvi
2.1 Relationships between different equilibrium concepts. 18
2.2 Relationships between different rationalizability concepts. 19
3.1 Relationships between different sets of axioms and
their representations. 29
7.1 An epistemic model for G"3 with corresponding ex-
tensive form T'3. 89
7.2 An epistemic model for IV 93
10.1 An epistemic model for the betting game. 131
12.1 Applying IECFA to "burning money'". 170 |
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| isbn | 0387262350 |
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| spelling | Asheim, Geir B. Verfasser (DE-588)170239039 aut Consistent preferences approach to deductive reasoning in games by Geir B. Asheim New York Springer 2006 XIX, 202 S. txt rdacontent n rdamedia nc rdacarrier Schlussfolgern (DE-588)4251178-1 gnd rswk-swf Widerspruchsfreiheit (DE-588)4189803-5 gnd rswk-swf Präferenz (DE-588)4121501-1 gnd rswk-swf Spieltheorie (DE-588)4056243-8 gnd rswk-swf Spieltheorie (DE-588)4056243-8 s Schlussfolgern (DE-588)4251178-1 s Präferenz (DE-588)4121501-1 s Widerspruchsfreiheit (DE-588)4189803-5 s b DE-604 Erscheint auch als Online-Ausgabe 0-387-26237-7 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014171257&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Asheim, Geir B. Consistent preferences approach to deductive reasoning in games Schlussfolgern (DE-588)4251178-1 gnd Widerspruchsfreiheit (DE-588)4189803-5 gnd Präferenz (DE-588)4121501-1 gnd Spieltheorie (DE-588)4056243-8 gnd |
| subject_GND | (DE-588)4251178-1 (DE-588)4189803-5 (DE-588)4121501-1 (DE-588)4056243-8 |
| title | Consistent preferences approach to deductive reasoning in games |
| title_auth | Consistent preferences approach to deductive reasoning in games |
| title_exact_search | Consistent preferences approach to deductive reasoning in games |
| title_exact_search_txtP | Consistent preferences approach to deductive reasoning in games |
| title_full | Consistent preferences approach to deductive reasoning in games by Geir B. Asheim |
| title_fullStr | Consistent preferences approach to deductive reasoning in games by Geir B. Asheim |
| title_full_unstemmed | Consistent preferences approach to deductive reasoning in games by Geir B. Asheim |
| title_short | Consistent preferences approach to deductive reasoning in games |
| title_sort | consistent preferences approach to deductive reasoning in games |
| topic | Schlussfolgern (DE-588)4251178-1 gnd Widerspruchsfreiheit (DE-588)4189803-5 gnd Präferenz (DE-588)4121501-1 gnd Spieltheorie (DE-588)4056243-8 gnd |
| topic_facet | Schlussfolgern Widerspruchsfreiheit Präferenz Spieltheorie |
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