Insights into game theory: an alternative mathematical experience
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2008
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 236 S. graph. Darst. |
| ISBN: | 9780521874229 9780521696920 |
Internformat
MARC
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| 245 | 1 | 0 | |a Insights into game theory |b an alternative mathematical experience |c Ein-Ya Gura and Michael Maschler |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2008 | |
| 300 | |a XIV, 236 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804137690762838016 |
|---|---|
| adam_text | Contents
Preface
page
xi
Introduction
xii
1
Mathematical Matching
1
1.1
Introduction
1
1.2
The Matching Problem
2
1.3
Exercises
7
1.4
Further Examples
10
1.5
Exercises
13
1.6
A Procedure for Finding Stable Matching Systems
(The Gale-Shapley Algorithm)
15
1.7
Exercises
18
1.8
A Stable Matching System Always Exists
19
1.9
The Maximum Number of Courtship Stages in the
Gale-Shapley Algorithm
21
1.10
Generalization
26
1.11
Exercises
33
1.12
The Gale-Shapley Algorithm and the
Assignment Problem
37
1.13
Exercises
40
1.14
Optimality
43
1.15
Exercises
49
1.16
Condition for the Existence of a Unique Stable
Matching System
52
1.17
Exercises
54
1.18
Discussion
55
1.19
Review Exercises
56
VIH
CONTENTS
2
Social
Justice
59
2.1
Presentation of the Problem
59
2.2
Mathematical Description of the Problem
62
2.3
Exercises
64
2.4
Social Choice Function
67
2.5
Axioms for the Social Choice Function
77
2.6
Exercises
80
2.7
What Follows from Axioms
1-4?
81
2.8
Exercises
85
2.9
Arrow s Theorem
87
2.10
What Next?
92
2.11
Review Exercises
93
3
The Shapley Value in Cooperative Games
97
3.1
Introduction
97
3.2
Cooperative Games
98
3.3
Important Examples of Coalition Function Games
101
3.4
Exercises
105
3.5
Additive Games
106
3.6 Superadditive
Games
107
3.7
Majority Games
108
3.8
Exercises
112
3.9
Symmetric Players
113
3.10
Exercises
115
3.11
Null Players
116
3.12
Exercises
117
3.13
The Sum of Games
118
3.14
Exercises
121
3.15
The Shapley Value
124
3.16
Exercises
133
3.17
Dissolving a Partnership
133
3.18
Exercises
141
CONTENTS
IX
3.19 The Shapley
Value as the Average of Players Marginal
Contributions
142
3.20
Exercises
146
3.21
The Shapley Value as a Player s Index of Power in
Weighted Majority Games
148
3.22
Exercises
153
3.23
The Shapley-Shubik Index as an Index for the
Analysis of Parliamentary Phenomena
153
3.24
Exercises
156
3.25
The Security Council
156
3.26
Exercises
158
3.27
Cost Games
159
3.28
Exercises
162
3.29
Review Exercises
164
4
Analysis of a Bankruptcy Problem from the Talmud
166
4.1
Introduction
166
4.2
The Contested Garment
168
4.3
Exercises
171
4.4
A Physical Interpretation of the Contested-Garment
Principle
172
4.5
Exercises
176
4.6
A Bankruptcy Problem from the Talmud
177
4.7
Exercises
180
4.8
Existence and Uniqueness
182
4.9
Divisions Consistent with the Contested-Garment
Principle
186
4.10
Exercises
191
4.11
Consistency
192
4.12
Exercises
194
4.13
Rif s Law of Division
194
4.14
Exercises
196
4.15
Proportional Division
196
X
CONTENTS
4.16
O Neill s Law of Division
197
4.17
Exercises
200
4.18
Discussion
201
4.19
Review Exercises
203
A Answers to the Exercises
205
A.1 Chapter
1 205
A.2 Chapter
2 213
A.3 Chapter
3 220
A.4 Chapter
4 229
Bibliography
233
Index
235
|
| adam_txt |
Contents
Preface
page
xi
Introduction
xii
1
Mathematical Matching
1
1.1
Introduction
1
1.2
The Matching Problem
2
1.3
Exercises
7
1.4
Further Examples
10
1.5
Exercises
13
1.6
A Procedure for Finding Stable Matching Systems
(The Gale-Shapley Algorithm)
15
1.7
Exercises
18
1.8
A Stable Matching System Always Exists
19
1.9
The Maximum Number of Courtship Stages in the
Gale-Shapley Algorithm
21
1.10
Generalization
26
1.11
Exercises
33
1.12
The Gale-Shapley Algorithm and the
Assignment Problem
37
1.13
Exercises
40
1.14
Optimality
43
1.15
Exercises
49
1.16
Condition for the Existence of a Unique Stable
Matching System
52
1.17
Exercises
54
1.18
Discussion
55
1.19
Review Exercises
56
VIH
CONTENTS
2
Social
Justice
59
2.1
Presentation of the Problem
59
2.2
Mathematical Description of the Problem
62
2.3
Exercises
64
2.4
Social Choice Function
67
2.5
Axioms for the Social Choice Function
77
2.6
Exercises
80
2.7
What Follows from Axioms
1-4?
81
2.8
Exercises
85
2.9
Arrow's Theorem
87
2.10
What Next?
92
2.11
Review Exercises
93
3
The Shapley Value in Cooperative Games
97
3.1
Introduction
97
3.2
Cooperative Games
98
3.3
Important Examples of Coalition Function Games
101
3.4
Exercises
105
3.5
Additive Games
106
3.6 Superadditive
Games
107
3.7
Majority Games
108
3.8
Exercises
112
3.9
Symmetric Players
113
3.10
Exercises
115
3.11
Null Players
116
3.12
Exercises
117
3.13
The Sum of Games
118
3.14
Exercises
121
3.15
The Shapley Value
124
3.16
Exercises
133
3.17
Dissolving a Partnership
133
3.18
Exercises
141
CONTENTS
IX
3.19 The Shapley
Value as the Average of Players' Marginal
Contributions
142
3.20
Exercises
146
3.21
The Shapley Value as a Player's Index of Power in
Weighted Majority Games
148
3.22
Exercises
153
3.23
The Shapley-Shubik Index as an Index for the
Analysis of Parliamentary Phenomena
153
3.24
Exercises
156
3.25
The Security Council
156
3.26
Exercises
158
3.27
Cost Games
159
3.28
Exercises
162
3.29
Review Exercises
164
4
Analysis of a Bankruptcy Problem from the Talmud
166
4.1
Introduction
166
4.2
The Contested Garment
168
4.3
Exercises
171
4.4
A Physical Interpretation of the Contested-Garment
Principle
172
4.5
Exercises
176
4.6
A Bankruptcy Problem from the Talmud
177
4.7
Exercises
180
4.8
Existence and Uniqueness
182
4.9
Divisions Consistent with the Contested-Garment
Principle
186
4.10
Exercises
191
4.11
Consistency
192
4.12
Exercises
194
4.13
Rif's Law of Division
194
4.14
Exercises
196
4.15
Proportional Division
196
X
CONTENTS
4.16
O'Neill's Law of Division
197
4.17
Exercises
200
4.18
Discussion
201
4.19
Review Exercises
203
A Answers to the Exercises
205
A.1 Chapter
1 205
A.2 Chapter
2 213
A.3 Chapter
3 220
A.4 Chapter
4 229
Bibliography
233
Index
235 |
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| index_date | 2024-07-02T21:00:51Z |
| indexdate | 2024-07-09T21:16:18Z |
| institution | BVB |
| isbn | 9780521874229 9780521696920 |
| language | English |
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| spelling | Gura, Ein-Ya Verfasser (DE-588)139752420 aut Insights into game theory an alternative mathematical experience Ein-Ya Gura and Michael Maschler 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2008 XIV, 236 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Game theory Social sciences / Methodology Sozialwissenschaften Spieltheorie (DE-588)4056243-8 gnd rswk-swf Spieltheorie (DE-588)4056243-8 s DE-604 Mashler, Mikhaʾel 1927-2008 Verfasser (DE-588)119158108 aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016522648&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gura, Ein-Ya Mashler, Mikhaʾel 1927-2008 Insights into game theory an alternative mathematical experience Game theory Social sciences / Methodology Sozialwissenschaften Spieltheorie (DE-588)4056243-8 gnd |
| subject_GND | (DE-588)4056243-8 |
| title | Insights into game theory an alternative mathematical experience |
| title_auth | Insights into game theory an alternative mathematical experience |
| title_exact_search | Insights into game theory an alternative mathematical experience |
| title_exact_search_txtP | Insights into game theory an alternative mathematical experience |
| title_full | Insights into game theory an alternative mathematical experience Ein-Ya Gura and Michael Maschler |
| title_fullStr | Insights into game theory an alternative mathematical experience Ein-Ya Gura and Michael Maschler |
| title_full_unstemmed | Insights into game theory an alternative mathematical experience Ein-Ya Gura and Michael Maschler |
| title_short | Insights into game theory |
| title_sort | insights into game theory an alternative mathematical experience |
| title_sub | an alternative mathematical experience |
| topic | Game theory Social sciences / Methodology Sozialwissenschaften Spieltheorie (DE-588)4056243-8 gnd |
| topic_facet | Game theory Social sciences / Methodology Sozialwissenschaften Spieltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016522648&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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