Cooperative games on combinatorial structures:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Kluwer
2000
|
| Series: | [Theory and decision library / C]
26 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 326 S. graph. Darst. |
| ISBN: | 0792377826 |
Staff View
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Record in the Search Index
| _version_ | 1804127814834716672 |
|---|---|
| adam_text | IMAGE 1
COOPERATIVE GAMES ON
COMBINATORIAL STRUCTURES
BY
JESUS MARIO BILBAO
UNIVERSITY OFSEVILLE
SPAIN
KLUWER ACADEMIC PUBLISHERS BOSTON / DORDRECHT / LONDON
IMAGE 2
CONTENTS
PREFACE IX
1 STRUCTURES 1
1.1 COOPERATIVE GAMES 1
1.2 GRAPH THEORY 7
1.3 EXAMPLES OF COOPERATIVE GAMES 10
1.4 CLOSURE SPACES AND CONVEX GEOMETRIES 15
1.5 MATROIDS, GREEDOIDS AND ANTIMATROIDS 18
1.6 PROJECT: BICOOPERATIVE GAMES 23
2 LINEAR OPTIMIZATION METHODS 27
2.1 POLYHEDRA 27
2.2 LINEAR PROGRAMMING 32
2.3 INTEGER AND COMBINATORIAI OPTIMIZATION 38
2.4 BALANCED GAMES . 46
2.5 THE GREEDY ALGORITHM 52
2.6 POLYMATROIDS 57
3 DISCRETE CONVEX ANALYSIS 65
3.1 FENCHEL CONJUGATION 65
3.2 SUBGRADIENTS AND SUBDIFFERENTIALS 70
3.3 INDIRECT FUNCTIONS OF COOPERATIVE GAMES 75
3.4 THE LEAST INCREMENT FUNCTION 80
3.5 THE LOVASZ EXTENSION OF GAMES 82
4 COMPUTATIONAL COMPLEXITY 89
4.1 MODELS OF COMPUTATION 90
4.2 THE COMPLEXITY CLASSES P AND NP 91
4.3 NP-COMPLETENESS AND #P-COMPLETENESS 98
4.4 COMPLEXITY IN COOPERATIVE GAME THEORY 101
4.5 PROJECT: LOCALLY CONCAVE (CONVEX) GAMES 105
IMAGE 3
VI CONTENTS
5 RESTRICTED GAMES BY PARTITION SYSTEMS 111
5.1 PARTITION SYSTEMS 112
5.2 ;F-RESTRICTED GAMES 113
5.3 THE CORE OF RESTRICTED GAMES 114
5.4 HART AND MAS-COLELL POTENTIAL 119
5.5 THE SHAPLEY AND BANZHAF VALUES 122
6 RESTRICTED GAMES BY UNION STABLE SYSTEMS 129
6.1 UNION STABLE SYSTEMS 130
6.2 COMPONENTS OF SETS 133
6.3 THE MYERSON VALUE 135
6.4 THE POSITION VALUE 142
6.5 CONVEXITY OF THE CONFERENCE GAME 150
6.6 PROJECT: SOLUTION CONTINUATION GAMES 154
7 VALUES FOR GAMES ON CONVEX GEOMETRIES 157
7.1 GAMES ON CONVEX GEOMETRIES 158
7.2 PROBABILISTIC VALUES FOR GAMES 160
7.3 EFFICIENCY AND COMPATIBLE-ORDER VALUES 165
7.4 AXIOMS FOR THE SHAPLEY VALUE 170
7.5 AXIOMS FOR THE BANZHAF INDEX 173
7.6 PROJECT: MARGINALIST AND EFFICIENT VALUES 180
8 VALUES FOR GAMES ON MATROIDS 181
8.1 THE RANK GAME 181
8.2 THE SHAPLEY VALUE FOR GAMES ON MATROIDS 185
8.3 QUASI-PROBABILISTIC VALUES 193
8.4 THE PROBABILISTIC SHAPLEY VALUE 198
9 THE CORE, THE SELECTOPE AND THE WEBER SET 205
9.1 THE CORE 205
9.2 THE SELECTOPE 208
9.3 THE WEBER SET 217
9.4 CONVEX AND QUASI-CONVEX GAMES 225
9.5 MARGINAL OPERATORS 233
10 SIMPLE GAMES ON CLOSURE SPACES 237
10.1 MINIMAL WINNING COALITIONS 237
10.2 THE CORE 240
10.3 THE WEBER SET 242
10.4 STABLE SETS 244
10.5 BARGAINING SETS 246
IMAGE 4
CONTENTS VII
11 VOTING POWER 253
11.1 WEIGHTED VOTING GAMES 253
11.2 GENERATING FUNCTIONS 255
11.3 COMPUTATIONAL COMPLEXITY 258
11.4 ALGORITHMS WITH MATHEMATICA 260
11.5 POWER IN 2-WEIGHTED VOTING GAMES 265
12 COMPUTING VALUES WITH MATHEMATICA 271
12.1 COMPUTING VALUES OF RESTRICTED GAMES 271
12.2 COMPUTING CONVEX SHAPLEY VALUES 277
12.3 COMPUTING CONVEX BANZHAF INDICES 283
12.4 THE BANZHAF POWER IN THE EUROPEAN UNION 288
12.5 COMPUTING THE NUMBER OF SUBTREES 290
12.6 THE MYERSON VALUE IN THE EUROPEAN UNION 296
BIBLIOGRAPHY 303
INDEX 321
|
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| dewey-raw | 519.3 |
| dewey-search | 519.3 |
| dewey-sort | 3519.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:39:20Z |
| institution | BVB |
| isbn | 0792377826 |
| language | English |
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| physical | X, 326 S. graph. Darst. |
| publishDate | 2000 |
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| publishDateSort | 2000 |
| publisher | Kluwer |
| record_format | marc |
| series2 | [Theory and decision library / C] |
| spelling | Bilbao, Jesús Mario Verfasser aut Cooperative games on combinatorial structures by Jesús Mario Bilbao Boston [u.a.] Kluwer 2000 X, 326 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier [Theory and decision library / C] 26 Combinatieleer gtt Speltheorie gtt TEORIA DOS JOGOS larpcal Combinatorial analysis Game theory Spieltheorie (DE-588)4056243-8 gnd rswk-swf Kombinatorische Analysis (DE-588)4164746-4 gnd rswk-swf Spieltheorie (DE-588)4056243-8 s Kombinatorische Analysis (DE-588)4164746-4 s DE-604 C] [Theory and decision library 26 (DE-604)BV000736902 26 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008935847&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bilbao, Jesús Mario Cooperative games on combinatorial structures Combinatieleer gtt Speltheorie gtt TEORIA DOS JOGOS larpcal Combinatorial analysis Game theory Spieltheorie (DE-588)4056243-8 gnd Kombinatorische Analysis (DE-588)4164746-4 gnd |
| subject_GND | (DE-588)4056243-8 (DE-588)4164746-4 |
| title | Cooperative games on combinatorial structures |
| title_auth | Cooperative games on combinatorial structures |
| title_exact_search | Cooperative games on combinatorial structures |
| title_full | Cooperative games on combinatorial structures by Jesús Mario Bilbao |
| title_fullStr | Cooperative games on combinatorial structures by Jesús Mario Bilbao |
| title_full_unstemmed | Cooperative games on combinatorial structures by Jesús Mario Bilbao |
| title_short | Cooperative games on combinatorial structures |
| title_sort | cooperative games on combinatorial structures |
| topic | Combinatieleer gtt Speltheorie gtt TEORIA DOS JOGOS larpcal Combinatorial analysis Game theory Spieltheorie (DE-588)4056243-8 gnd Kombinatorische Analysis (DE-588)4164746-4 gnd |
| topic_facet | Combinatieleer Speltheorie TEORIA DOS JOGOS Combinatorial analysis Game theory Spieltheorie Kombinatorische Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008935847&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000736902 |
| work_keys_str_mv | AT bilbaojesusmario cooperativegamesoncombinatorialstructures |