Game theory: a multi-leveled approach
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Heidelberg
Springer
[2015]
|
| Edition: | Second edition |
| Series: | Springer texts in business and economics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xvii, 494 Seiten Diagramme 235 mm x 155 mm |
| ISBN: | 9783662469491 3662469499 |
Staff View
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Record in the Search Index
| _version_ | 1804153302580985856 |
|---|---|
| adam_text | CONTENTS
1 INTRODUCTION 1
1.1 A DEFINITION 1
1.2 SOME HISTORY 1
1.3 EXAMPLES 3
1.3.1 ZERO-SUM GAMES 3
1.3.2 NONZERO-SUM GAMES 6
1.3.3 EXTENSIVE FORM GAMES 8
1.3.4 COOPERATIVE GAMES 12
1.3.5 BARGAINING GAMES 16
1.4 COOPERATIVE VERSUS NONCOOPERATIVE GAME THEORY 17
1.5 PROBLEMS 17
1.6 NOTES 19
REFERENCES 20
PART I THINKING STRATEGICALLY
2 FINITE TWO-PERSON ZERO-SUM GAMES 25
2.1 BASIC DEFINITIONS AND THEORY 25
2.2 SOLVING 2 X N
GAMES AND MX 2 GAMES 28
2.2.1 2 X N GAMES 28
2.2.2 MX 2 GAMES 30
2.2.3 STRICT DOMINATION 31
2.3 PROBLEMS 33
2.4 NOTES 35
REFERENCE 35
3 FINITE TWO-PERSON GAMES 37
3.1 BASIC DEFINITIONS AND THEORY 37
3.2 FINDING NASH EQUILIBRIA 39
3.2.1 PURE NASH EQUILIBRIA 40
3.2.2 2 X 2 GAMES 41
3.2.3 STRICT DOMINATION 42
XI
HTTP://D-NB.INFO/1068717882
XII CONTENTS
3.3 PROBLEMS 44
3.4 NOTES 49
REFERENCES 49
4 FINITE EXTENSIVE FORM GAMES 51
4.1 THE EXTENSIVE FORM 52
4.2 THE STRATEGIC FORM 54
4.3 BACKWARD INDUCTION AND SUBGAME PERFECTION 56
4.4 PERFECT BAYESIAN EQUILIBRIUM 60
4.5 PROBLEMS 63
4.6 NOTES 69
REFERENCES 69
5 FINITE GAMES WITH INCOMPLETE INFORMATION 71
5.1 PLAYER TYPES 72
5.2 STATIC GAMES OF INCOMPLETE INFORMATION 72
5.2.1 BATTLE-OF-THE-SEXES WITH ONE-SIDED
INCOMPLETE INFORMATION 73
5.2.2 BATTLE-OF-THE-SEXES WITH TWO-SIDED
INCOMPLETE INFORMATION 75
5.3 SIGNALING GAMES 78
5.3.1 AN EXAMPLE 78
5.3.2 COMPUTING PERFECT BAYESIAN EQUILIBRIA
IN THE EXTENSIVE FORM 81
5.3.3 THE INTUITIVE CRITERION 81
5.3.4 ANOTHER EXAMPLE 82
5.4 PROBLEMS 83
5.5 NOTES . 88
REFERENCES 88
6 NONCOOPERATIVE GAMES: EXTENSIONS 89
6.1 GENERAL FRAMEWORK: STRATEGIC GAMES 90
6.2 COURNOT QUANTITY COMPETITION 91
6.2.1 SIMPLE VERSION WITH COMPLETE INFORMATION 91
6.2.2 SIMPLE VERSION WITH INCOMPLETE INFORMATION 93
6.3 BERTRAND PRICE COMPETITION 95
6.4 STACKELBERG EQUILIBRIUM 98
6.5 AUCTIONS 99
6.5.1 COMPLETE INFORMATION 100
6.5.2 INCOMPLETE INFORMATION 101
6.5.3 INCOMPLETE INFORMATION: A DOUBLE AUCTION 102
6.6 MIXED STRATEGIES AND INCOMPLETE INFORMATION 103
6.7 SEQUENTIAL BARGAINING 105
6.7.1 FINITE HORIZON BARGAINING 106
6.7.2 INFINITE HORIZON BARGAINING 108
CONTENTS XIII
6.8 PROBLEMS 110
6.9 NOTES 119
REFERENCES 120
7 REPEATED GAMES 121
7.1 SUBGAME PERFECT EQUILIBRIUM 121
7.1.1 THE PRISONERS DILEMMA 121
7.1.2 SOME GENERAL OBSERVATIONS 126
7.1.3 ANOTHER EXAMPLE 128
7.2 NASH EQUILIBRIUM 130
7.2.1 AN EXAMPLE 130
7.2.2 A FOLK THEOREM FOR NASH EQUILIBRIUM 132
7.2.3 ANOTHER EXAMPLE 133
7.3 PROBLEMS 135
7.4 NOTES -. 138
REFERENCES 138
8 AN INTRODUCTION TO EVOLUTIONARY GAMES 139
8.1 SYMMETRIC TWO-PLAYER GAMES AND EVOLUTIONARY
STABLE STRATEGIES 139
8.2 REPLICATOR DYNAMICS AND EVOLUTIONARY STABILITY 142
8.3 ASYMMETRIC GAMES 145
8.4 PROBLEMS 147
8.5 NOTES 149
REFERENCES 150
9 COOPERATIVE GAMES WITH TRANSFERABLE UTILITY 151
9.1 EXAMPLES AND PRELIMINARIES 151
9.2 THE CORE 153
9.3 THE SHAPLEY VALUE 156
9.4 THE NUCLEOLUS 159
9.5 PROBLEMS 165
9.6 NOTES 169
REFERENCES 169
10 COOPERATIVE GAME MODELS 171
10.1 BARGAINING PROBLEMS 171
10.1.1 THE NASH BARGAINING SOLUTION 172
10.1.2 RELATION WITH THE RUBINSTEIN BARGAINING PROCEDURE 176
10.2 EXCHANGE ECONOMIES 178
10.3 MATCHING PROBLEMS 182
10.4 HOUSE EXCHANGE 185
10.5 PROBLEMS 186
10.6 NOTES 190
REFERENCES 191
XIV CONTENTS
11 SOCIAL CHOICE 193
11.1 INTRODUCTION AND PRELIMINARIES 193
11.1.1 AN EXAMPLE 193
11.1.2 PRELIMINARIES 195
11.2 ARROW S THEOREM 196
11.3 THE GIBBARD-SATTERTHWAITE THEOREM 199
11.4 PROBLEMS 201
11.5 NOTES 202
REFERENCES 203
PART II NONCOOPERATIVE GAMES
12 MATRIX GAMES 207
12.1 THE MINIMAX THEOREM 207
12.2 A LINEAR PROGRAMMING FORMULATION ~ 209
12.3 PROBLEMS 211
12.4 NOTES 213
REFERENCES 213
13 FINITE GAMES 215
13.1 EXISTENCE OF NASH EQUILIBRIUM 215
13.2 BIMATRIX GAMES 217
13.2.1 PURE AND MIXED STRATEGIES IN NASH EQUILIBRIUM 217
13.2.2 EXTENSION OF THE GRAPHICAL METHOD 219
13.2.3 A MATHEMATICAL PROGRAMMING APPROACH 221
13.2.4 MATRIX GAMES 222
13.2.5 THE GAME OF CHESS: ZERMELO S THEOREM 223
13.3 ITERATED DOMINANCE AND BEST REPLY 224
13.4 PERFECT EQUILIBRIUM 227
13.5 PROPER EQUILIBRIUM 233
13.6 STRICTLY PERFECT EQUILIBRIUM 235
13.7 CORRELATED EQUILIBRIUM 236
13.8 A CHARACTERIZATION OF NASH EQUILIBRIUM 240
13.9 PROBLEMS 243
13.10 NOTES 248
REFERENCES 249
14 EXTENSIVE FORM GAMES 251
14.1 EXTENSIVE FORM STRUCTURES AND GAMES 251
14.2 PURE, MIXED AND BEHAVIORAL STRATEGIES 253
14.3 NASH EQUILIBRIUM AND REFINEMENTS 256
14.3.1 SUBGAME PERFECT EQUILIBRIUM 258
14.3.2 PERFECT BAYESIAN AND SEQUENTIAL EQUILIBRIUM 259
14.4 PROBLEMS 266
14.5 NOTES 270
REFERENCES 271
CONTENTS XV
15 EVOLUTIONARY GAMES 273
15.1 SYMMETRIC TWO-PLAYER GAMES 273
15.1.1 SYMMETRIC 2 X 2-GAMES 274
15.2 EVOLUTIONARY STABILITY 274
15.2.1 EVOLUTIONARY STABLE STRATEGIES 274
15.2.2 THE STRUCTURE OF THE SET ESS(A) 276
15.2.3 RELATIONS WITH OTHER REFINEMENTS 276
15.2.4 OTHER CHARACTERIZATIONS OF ESS 276
15.3 REPLICATOR DYNAMICS AND ESS 279
15.3.1 REPLICATOR DYNAMICS 279
15.3.2 SYMMETRIC 2 X 2 GAMES 280
15.3.3 DOMINATED STRATEGIES 281
15.3.4 NASH EQUILIBRIUM STRATEGIES 282
15.3.5 PERFECT EQUILIBRIUM STRATEGIES 283
15.4 PROBLEMS 285
15.5 NOTES 287
REFERENCES 288
PART III COOPERATIVE GAMES
16 TU-GAMES: DOMINATION, STABLE SETS, AND THE CORE 291
16.1 IMPUTATIONS AND DOMINATION 291
16.2 THE CORE AND THE DOMINATION-CORE 293
16.3 SIMPLE GAMES 295
16.4 STABLE SETS 296
16.5 BALANCED GAMES AND THE CORE 298
16.6 PROBLEMS 300
16.7 NOTES 302
REFERENCES 302
17 THE SHAPLEY VALUE 305
17.1 DEFINITION AND SHAPLEY S CHARACTERIZATION 305
17.2 OTHER CHARACTERIZATIONS 311
17.2.1 DIVIDENDS 311
17.2.2 STRONG MONOTONICITY 312
17.2.3 MULTILINEAR EXTENSION 313
17.3 POTENTIAL AND REDUCED GAME 315
17.3.1 THE POTENTIAL APPROACH TO THE SHAPLEY VALUE 315
17.3.2 REDUCED GAMES 318
17.4 PROBLEMS 323
17.5 NOTES 324
REFERENCES 325
18 CORE, SHAPLEY VALUE, AND WEBER SET 327
18.1 THE WEBER SET 327
18.2 CONVEX GAMES 329
XVI CONTENTS
18.3 RANDOM ORDER VALUES 331
18.4 WEIGHTED SHAPLEY VALUES 337
18.5 PROBLEMS 340
18.6 NOTES 341
REFERENCES 342
19 THE NUCLEOLUS 343
19.1 AN EXAMPLE 343
19.2 THE LEXICOGRAPHIC ORDER 345
19.3 THE (PRE-)NUCLEOLUS 345
19.4 THE KOHLBERG CRITERION 347
19.5 COMPUTATION OF THE NUCLEOLUS 350
19.6 A CHARACTERIZATION OF THE PRE-NUCLEOLUS 353
19.7 PROBLEMS 355
19.8 NOTES 358
REFERENCES 358
20 SPECIAL TRANSFERABLE UTILITY GAMES 361
20.1 ASSIGNMENT AND PERMUTATION GAMES 361
20.2 FLOW GAMES 365
20.3 VOTING GAMES: THE BANZHAF VALUE 367
20.4 PROBLEMS 370
20.5 NOTES 372
REFERENCES 373
21 BARGAINING PROBLEMS 375
21.1 THE BARGAINING PROBLEM 375
21.2 THE RAIFFA-KALAI-SMORODINSKY SOLUTION 377
21.3 THE EGALITARIAN SOLUTION 379
21.4 NONCOOPERATIVE BARGAINING 381
21.5 GAMES WITH NONTRANSFERABLE UTILITY 382
21.6 PROBLEMS 382
21.7 NOTES 385
REFERENCES 385
PART IV TOOLS, HINTS AND SOLUTIONS
22 TOOLS 389
22.1 SOME DEFINITIONS 389
22.2 A SEPARATION THEOREM 390
22.3 LEMMAS OF THE ALTERNATIVE 391
22.4 THE DUALITY THEOREM OF LINEAR PROGRAMMING 393
22.5 SOME FIXED POINT THEOREMS 394
22.6 THE BIRKHOFF-VON NEUMANN THEOREM 395
22.7 THE MAX-FLOW MIN-CUT THEOREM 397
CONTENTS XVII
22.8 PROBLEMS 401
22.9 NOTES 401
REFERENCES 402
23 REVIEW PROBLEMS FOR PART I 403
REFERENCES 423
24 HINTS, ANSWERS AND SOLUTIONS 425
REFERENCE 483
REFERENCES 485
INDEX 491
|
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| language | English |
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| spelling | Peters, Hans J. M. 1953- Verfasser (DE-588)124306349 aut Game theory a multi-leveled approach Hans Peters Second edition Heidelberg Springer [2015] xvii, 494 Seiten Diagramme 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Springer texts in business and economics Spieltheorie (DE-588)4056243-8 gnd rswk-swf Wirtschaftswissenschaften (DE-588)4066528-8 gnd rswk-swf Wirtschaftswissenschaften (DE-588)4066528-8 s Spieltheorie (DE-588)4056243-8 s 1\p DE-604 Erscheint auch als Online-Ausgabe 978-3-662-46950-7 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027973583&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Peters, Hans J. M. 1953- Game theory a multi-leveled approach Spieltheorie (DE-588)4056243-8 gnd Wirtschaftswissenschaften (DE-588)4066528-8 gnd |
| subject_GND | (DE-588)4056243-8 (DE-588)4066528-8 |
| title | Game theory a multi-leveled approach |
| title_auth | Game theory a multi-leveled approach |
| title_exact_search | Game theory a multi-leveled approach |
| title_full | Game theory a multi-leveled approach Hans Peters |
| title_fullStr | Game theory a multi-leveled approach Hans Peters |
| title_full_unstemmed | Game theory a multi-leveled approach Hans Peters |
| title_short | Game theory |
| title_sort | game theory a multi leveled approach |
| title_sub | a multi-leveled approach |
| topic | Spieltheorie (DE-588)4056243-8 gnd Wirtschaftswissenschaften (DE-588)4066528-8 gnd |
| topic_facet | Spieltheorie Wirtschaftswissenschaften |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027973583&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT petershansjm gametheoryamultileveledapproach |