Social and economic networks in cooperative game theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Kluwer Academic Publ.
2001
|
| Series: | Theory and decision library
Series C, Game theory, mathematical programming and operations research ; 27 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 291 S. graph. Darst. |
| ISBN: | 0792372263 |
Staff View
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Record in the Search Index
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| adam_text | Contents
Preface ix
Part I Social and Economic Networks in Cooperative Situations
1. GAMES AND NETWORKS 3
1.1 Coalitional games 3
1.2 Networks 13
2. RESTRICTED COOPERATION IN GAMES 21
2.1 Games with restricted communication 21
2.2 The Myerson value 29
2.3 Other allocation rules 43
3. INHERITANCE OP PROPERTIES IN COMMUNICATION
SITUATIONS 53
3.1 Superadditivity 54
3.2 Balancedness and totally balancedness 55
3.3 Convexity 58
3.4 Average convexity 62
3.5 Core-inclusion of the Shapley value 73
3.6 Population monotonic allocation schemes 81
3.7 Review and remarks 86
4. VARIANTS ON THE BASIC MODEL 89
4.1 Games with coalition structures 90
4.2 Hypergraph communication situations 95
4.3 Probabilistic communication situations 100
4.4 NTU communication situations 107
4.5 Reward communication situations 115
4.6 Directed communication situations 124
vi NETWORKS IN COOPERATIVE GAME THEORY
Part II Network Formation
5. NONCOOPERATIVE GAMES 135
5.1 Games in extensive form 135
5.2 Games in strategic form 140
6. A NETWORK-FORMATION MODEL IN EXTENSIVE FORM 153
6.1 Description of the model 153
6.2 Some examples 155
6.3 Weighted majority games 160
6.4 Symmetric convex games 164
7. A NETWORK-FORMATION MODEL IN STRATEGIC FORM 173
7.1 Description of the model 174
7.2 Nash equilibrium and strong Nash equilibrium 179
7.3 Undominated Nash equilibrium and coalition-proof Nash
equilibrium 183
7.4 Comparison of the network-formation models 189
7.5 Remarks 190
8. NETWORK FORMATION WITH COSTS FOR ESTABLISHING
LINKS 193
8.1 The cost-extended Myerson value 193
8.2 Network-formation games in extensive form 198
8.3 Network-formation games in strategic form 202
8.3.1 Nash equilibrium and strong Nash equilibrium 203
8.3.2 Undominated Nash equilibrium 205
8.3.3 Coalition-proof Nash equilibrium 206
8.4 Extensions 209
8.5 Comparison of the network-formation models 210
9. A ONE-STAGE MODEL OF NETWORK FORMATION AND
PAYOFF DIVISION 213
9.1 The model 213
9.2 Nash equilibrium 218
9.3 Strong Nash equilibrium 223
9.4 Coalition-proof Nash equilibrium 229
10.NETWORK FORMATION AND POTENTIAL GAMES 249
10.1 Potential games 249
10.2 A representation theorem 254
10.3 Network formation 257
10.4 Remarks 262
ll.NETWORK FORMATION AND REWARD FUNCTIONS 265
11.1 Pairwise stability 265
11.2 Weak and strong stability 271
11.3 Dynamic models of network formation 276
References 281
Notations 287
Index 289
|
| adam_txt |
Contents
Preface ix
Part I Social and Economic Networks in Cooperative Situations
1. GAMES AND NETWORKS 3
1.1 Coalitional games 3
1.2 Networks 13
2. RESTRICTED COOPERATION IN GAMES 21
2.1 Games with restricted communication 21
2.2 The Myerson value 29
2.3 Other allocation rules 43
3. INHERITANCE OP PROPERTIES IN COMMUNICATION
SITUATIONS 53
3.1 Superadditivity 54
3.2 Balancedness and totally balancedness 55
3.3 Convexity 58
3.4 Average convexity 62
3.5 Core-inclusion of the Shapley value 73
3.6 Population monotonic allocation schemes 81
3.7 Review and remarks 86
4. VARIANTS ON THE BASIC MODEL 89
4.1 Games with coalition structures 90
4.2 Hypergraph communication situations 95
4.3 Probabilistic communication situations 100
4.4 NTU communication situations 107
4.5 Reward communication situations 115
4.6 Directed communication situations 124
vi NETWORKS IN COOPERATIVE GAME THEORY
Part II Network Formation
5. NONCOOPERATIVE GAMES 135
5.1 Games in extensive form 135
5.2 Games in strategic form 140
6. A NETWORK-FORMATION MODEL IN EXTENSIVE FORM 153
6.1 Description of the model 153
6.2 Some examples 155
6.3 Weighted majority games 160
6.4 Symmetric convex games 164
7. A NETWORK-FORMATION MODEL IN STRATEGIC FORM 173
7.1 Description of the model 174
7.2 Nash equilibrium and strong Nash equilibrium 179
7.3 Undominated Nash equilibrium and coalition-proof Nash
equilibrium 183
7.4 Comparison of the network-formation models 189
7.5 Remarks 190
8. NETWORK FORMATION WITH COSTS FOR ESTABLISHING
LINKS 193
8.1 The cost-extended Myerson value 193
8.2 Network-formation games in extensive form 198
8.3 Network-formation games in strategic form 202
8.3.1 Nash equilibrium and strong Nash equilibrium 203
8.3.2 Undominated Nash equilibrium 205
8.3.3 Coalition-proof Nash equilibrium 206
8.4 Extensions 209
8.5 Comparison of the network-formation models 210
9. A ONE-STAGE MODEL OF NETWORK FORMATION AND
PAYOFF DIVISION 213
9.1 The model 213
9.2 Nash equilibrium 218
9.3 Strong Nash equilibrium 223
9.4 Coalition-proof Nash equilibrium 229
10.NETWORK FORMATION AND POTENTIAL GAMES 249
10.1 Potential games 249
10.2 A representation theorem 254
10.3 Network formation 257
10.4 Remarks 262
ll.NETWORK FORMATION AND REWARD FUNCTIONS 265
11.1 Pairwise stability 265
11.2 Weak and strong stability 271
11.3 Dynamic models of network formation 276
References 281
Notations 287
Index 289 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T20:16:59Z |
| indexdate | 2024-07-09T21:13:28Z |
| institution | BVB |
| isbn | 0792372263 |
| language | English |
| lccn | 00102918 |
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| physical | XI, 291 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Kluwer Academic Publ. |
| record_format | marc |
| series | Theory and decision library |
| series2 | Theory and decision library : Series C, Game theory, mathematical programming and operations research |
| spelling | Slikker, Marco Verfasser aut Social and economic networks in cooperative game theory by Marco Slikker and Anne van den Nouweland Boston [u.a.] Kluwer Academic Publ. 2001 XI, 291 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Theory and decision library : Series C, Game theory, mathematical programming and operations research 27 Kooperatives Spiel / Business Network / Theorie Social networks Business networks Game theory Spieltheorie (DE-588)4056243-8 gnd rswk-swf Netzwerk (DE-588)4171529-9 gnd rswk-swf Spieltheorie (DE-588)4056243-8 s Netzwerk (DE-588)4171529-9 s DE-604 Nouweland, Anne van den Verfasser aut Theory and decision library Series C, Game theory, mathematical programming and operations research ; 27 (DE-604)BV000736902 27 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016409296&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Slikker, Marco Nouweland, Anne van den Social and economic networks in cooperative game theory Theory and decision library Kooperatives Spiel / Business Network / Theorie Social networks Business networks Game theory Spieltheorie (DE-588)4056243-8 gnd Netzwerk (DE-588)4171529-9 gnd |
| subject_GND | (DE-588)4056243-8 (DE-588)4171529-9 |
| title | Social and economic networks in cooperative game theory |
| title_auth | Social and economic networks in cooperative game theory |
| title_exact_search | Social and economic networks in cooperative game theory |
| title_exact_search_txtP | Social and economic networks in cooperative game theory |
| title_full | Social and economic networks in cooperative game theory by Marco Slikker and Anne van den Nouweland |
| title_fullStr | Social and economic networks in cooperative game theory by Marco Slikker and Anne van den Nouweland |
| title_full_unstemmed | Social and economic networks in cooperative game theory by Marco Slikker and Anne van den Nouweland |
| title_short | Social and economic networks in cooperative game theory |
| title_sort | social and economic networks in cooperative game theory |
| topic | Kooperatives Spiel / Business Network / Theorie Social networks Business networks Game theory Spieltheorie (DE-588)4056243-8 gnd Netzwerk (DE-588)4171529-9 gnd |
| topic_facet | Kooperatives Spiel / Business Network / Theorie Social networks Business networks Game theory Spieltheorie Netzwerk |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016409296&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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