The cooperative game theory of networks and hierarchies:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Heidelberg [u.a.]
Springer
2010
|
| Series: | Theory and decision library
Series C, Game theory, mathematical programming and operations research ; 44 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XI, 255 S. graph. Darst. |
| ISBN: | 9783642052811 |
Staff View
MARC
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| 245 | 1 | 0 | |a The cooperative game theory of networks and hierarchies |c Robert P. Gilles |
| 264 | 1 | |a Heidelberg [u.a.] |b Springer |c 2010 | |
| 300 | |a XI, 255 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Theory and decision library : Series C, Game theory, mathematical programming and operations research |v 44 | |
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| 650 | 4 | |a Organizational behavior | |
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Record in the Search Index
| _version_ | 1805093232814587904 |
|---|---|
| adam_text |
Contents
Cooperative
Game
Theory
. 1
1.1
Aims and Outline of the Book
. 2
1.2
Game Forms
. 5
1.2.1
The Normal Form
. 7
1.2.2
The Characteristic Function Form
. 9
1.3
Cooperative Games
. 12
1.3.1
Basic Properties of Cooperative Games
. 13
1.3.2
The Standard Basis
. 14
1.3.3
The Unanimity Basis
. 15
1.3.4
Essential Games and Imputations
. 18
1.4
Multilinear Extensions
. 20
1.5
Problems
. 25
The Core of a Cooperative Game
. 29
2.1
Basic Properties of the Core
. 30
2.1.1
Representing the Core of a Three Player Game
. 31
2.1.2
The Core and Domination
. 35
2.1.3
Existence of Core Imputations
. 37
2.2
The Core Based on a Collection of Coalitions
. 39
2.2.1
Balanced Collections
. 45
2.2.2
Strongly Balanced Collections
. 47
2.2.3
Lattices and Hierarchies
. 48
2.3
Core Covers and Convex Games
. 51
2.3.1
TheWeberSet
. 51
2.3.2
The Selectope
. 53
2.4
Appendix: Proofs of the Main Theorems
. 55
2.5
Problems
. 68
Axiomatic Value Theory
. 71
3.1
Equivalent Formulations of the Shapley Value
. 72
3.2
Three Axiomatizations of the Shapley Value
. 76
3.2.1
Shapley's Axiomatization
. 77
x
Contents
3.2.2
Young's Axiomatization
. 80
3.2.3
van den Brink's Axiomatization
. 82
3.3
The Shapley Value as a Utility Function
. 83
3.4
The Myerson Value
. 89
3.5
Appendix: Proofs of the Main Theorems
. 92
3.6
Problems
.101
4
The Cooperative Potential
.107
4.1
A Potential Function for Cooperative Games
.108
4.2
The Cooperative Potential and the Shapley Value
.112
4.3
Consistency and the Reductionist Approach
.115
4.4
Beyond the Cooperative Potential
.119
4.4.1
Value-Based Potentials
.119
4.4.2
Share Functions and Share Potentials
.122
4.5
Appendix: Proofs of the Main Theorems
.126
4.6
Problems
.138
5
Directed Communication Networks
.143
5.1
Directed Networks
.145
5.2
Measuring Dominance in Directed Networks
.147
5.2.1
The Degree Measure
.148
5.2.2
The
jß-Measure.151
5.2.3
Iterated Power Measures
.158
5.3
Hierarchical Allocation Rules on Network Games
.163
5.3.1
Cooperative Network Situations
.164
5.3.2
Network Myerson Values
.166
5.3.3
The Hierarchical Payoff Property
.168
5.3.4
The a-Hierarchical Value
.171
5.4
Appendix: Proofs of the Main Theorems
.175
5.5
Problems
.186
6
Cooperative Theories of Hierarchical Organizations
.189
6.1
Games with a Permission Structure
.191
6.1.1
The Conjunctive Approach
.194
6.1.2
The Disjunctive Approach
.198
6.2
Shapley Permission Values
.210
6.2.1
The Conjunctive Permission Value
.210
6.2.2
The Disjunctive Permission Value
.216
6.3
Modeling Economic Phenomena
.219
6.4
Appendix: Proofs of the Main Theorems
.222
6.5
Discussion: More About the Disjunctive Restriction
.237
6.6
Problems
.239
References
.245
Index
.251 |
| any_adam_object | 1 |
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| dewey-full | 519.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.3 |
| dewey-search | 519.3 |
| dewey-sort | 3519.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV035843512 |
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| indexdate | 2024-07-20T10:24:14Z |
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| isbn | 9783642052811 |
| language | English |
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| physical | XI, 255 S. graph. Darst. |
| publishDate | 2010 |
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| series | Theory and decision library |
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| spelling | Gilles, Robert Paul Verfasser (DE-588)170800903 aut The cooperative game theory of networks and hierarchies Robert P. Gilles Heidelberg [u.a.] Springer 2010 XI, 255 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Theory and decision library : Series C, Game theory, mathematical programming and operations research 44 Game theory Organizational behavior Social networks Kooperatives Spiel (DE-588)4120603-4 gnd rswk-swf Kooperatives Spiel (DE-588)4120603-4 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-05282-8 Theory and decision library Series C, Game theory, mathematical programming and operations research ; 44 (DE-604)BV000736902 44 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3365420&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018701766&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gilles, Robert Paul The cooperative game theory of networks and hierarchies Theory and decision library Game theory Organizational behavior Social networks Kooperatives Spiel (DE-588)4120603-4 gnd |
| subject_GND | (DE-588)4120603-4 |
| title | The cooperative game theory of networks and hierarchies |
| title_auth | The cooperative game theory of networks and hierarchies |
| title_exact_search | The cooperative game theory of networks and hierarchies |
| title_full | The cooperative game theory of networks and hierarchies Robert P. Gilles |
| title_fullStr | The cooperative game theory of networks and hierarchies Robert P. Gilles |
| title_full_unstemmed | The cooperative game theory of networks and hierarchies Robert P. Gilles |
| title_short | The cooperative game theory of networks and hierarchies |
| title_sort | the cooperative game theory of networks and hierarchies |
| topic | Game theory Organizational behavior Social networks Kooperatives Spiel (DE-588)4120603-4 gnd |
| topic_facet | Game theory Organizational behavior Social networks Kooperatives Spiel |
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