Introduction to game theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1994
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 223 - 225 |
| Beschreibung: | XVI, 230 S. graph. Darst. |
| ISBN: | 354094284X 038794284X |
Internformat
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| 100 | 1 | |a Morris, Peter |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to game theory |c Peter Morris |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1994 | |
| 300 | |a XVI, 230 S. |b graph. Darst. | ||
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Datensatz im Suchindex
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| adam_text |
PETER
MORRIS
INTRODUCTION
TO
GAME
THEORY
WITH
44 ILLUSTRATIONS
SPRINGER
CONTENTS
PREFACE VII
LIST OF FIGURES XV
1.
GAMES IN EXTENSIVE FORM 1
1.1. TREES 3
1.2. GAME TREES 7
1.2.1. INFORMATION SETS 11
1.3. CHOICE FUNCTIONS AND STRATEGIES 12
1.3.1. CHOICE SUBTREES 13
1.4. GAMES WITH CHANCE MOVES 20
1.4.1. A THEOREM ON PAYOFFS 22
1.5. EQUILIBRIUM IV-TUPLES OF STRATEGIES 24
1.6. NORMAL FORMS 29
2.
TWO-PERSON ZERO-SUM GAMES 35
2.1.
SADDLE POINTS 36
2.2.
MIXED STRATEGIES
#
40
2.2.1.
ROW VALUES AND COLUMN VALUES 43
2.2.2. DOMINATED ROWS AND COLUMNS 48
2.3.
SMALL GAMES 52
2.3.1.
2
X
N AND
M
X 2 GAMES 55
2.4. SYMMETRIC GAMES 59
2.4.1.
SOLVING SYMMETRIC GAMES 60
XII CONTENTS
3.
LINEAR PROGRAMMING 65
3.1.
PRIMAL AND DUAL PROBLEMS 65
3.1.1.
PRIMAL PROBLEMS AND THEIR DUALS 67
3.2. BASIC FORMS AND PIVOTS 71
3.2.1.
PIVOTS 72
3.2.2. DUAL BASIC FORMS 75
3.3.
THE SIMPLEX ALGORITHM 78
3.3.1.
TABLEAUS 78
3.3.2. THE SIMPLEX ALGORITHM 81
3.4. AVOIDING CYCLES AND ACHIEVING FEASIBILITY 85
3.4.1.
DEGENERACY AND CYCLES 85
3.4.2. THE INITIAL FEASIBLE TABLEAU 88
3.5.
DUALITY 91
3.5.1.
THE DUAL SIMPLEX ALGORITHM 92
3.5.2. THE DUALITY THEOREM 95
4.
SOLVING MATRIX GAMES 99
4.1.
THE MINIMAX THEOREM 99
4.2.
SOME EXAMPLES 104
4.2.1.
SCISSORS-PAPER-STONE 104
4.2.2.
THREE-FINGER MORRA 106
4.2.3.
COLONEL BLOTTO'S GAME 107
4.2.4. SIMPLE POKER 108
5. NON-ZERO-SUM GAMES 115
5.1.
NONCOOPERATIVE GAMES 116
5.1.1.
MIXED STRATEGIES 117
5.1.2. MAXIMIN VALUES 119
5.1.3.
EQUILIBRIUM N-TUPLES OF MIXED STRATEGIES 120
5.1.4.
A GRAPHICAL METHOD FOR COMPUTING EQUILIBRIUM PAIRS 121
5.2.
SOLUTION CONCEPTS FOR NONCOOPERATIVE GAMES 124
5.2.1.
BATTLE OF THE BUDDIES 126
5.2.2. PRISONER'S DILEMMA 127
5.2.3.
ANOTHER GAME 127
5.2.4.
SUPERGAMES 128
5.3.
COOPERATIVE GAMES 132
5.3.1.
NASH BARGAINING AXIOMS 134
5.3.2. CONVEX SETS 136
5.3.3.
NASH'S THEOREM 138
CONTENTS XIII
5.3.4. COMPUTING ARBITRATION PAIRS 143
5.3.5. REMARKS 145
6. N-PERSON COOPERATIVE GAMES 149
6.1.
COALITIONS 149
6.1.1.
THE CHARACTERISTIC FUNCTION 150
6.1.2. ESSENTIAL AND INESSENTIAL GAMES 154
6.2. IMPUTATIONS 156
6.2.1.
DOMINANCE OF IMPUTATIONS 158
6.2.2. THE CORE 159
6.2.3.
CONSTANT-SUM GAMES 163
6.2.4. A VOTING GAME 165
6.3.
STRATEGIC EQUIVALENCE 167
6.3.1.
EQUIVALENCE AND IMPUTATIONS 169
6.3.2. (O,L)-REDUCED FORM 170
6.3.3.
CLASSIFICATION OF SMALL GAMES 172
6.4. TWO SOLUTION CONCEPTS 174
6.4.1.
STABLE SETS OF IMPUTATIONS 174
6.4.2. SHAPLEY VALUES 178
7. GAME-PLAYING PROGRAMS 185
7.1.
THREE ALGORITHMS 186
7.1.1.
THE NAIVE ALGORITHM 186
7.1.2. THE BRANCH AND BOUND ALGORITHM 187
7.1.3.
THE ALPHA-BETA PRUNING ALGORITHM 189
7.2. EVALUATION FUNCTIONS 191
7.2.1.
DEPTH-LIMITED SUBGAMES 192
7.2.2. MANCALA 194
7.2.3.
NINE-MEN'S MORRIS 197
APPENDIX. SOLUTIONS 201
BIBLIOGRAPHY 223
INDEX 227 |
| any_adam_object | 1 |
| author | Morris, Peter |
| author_facet | Morris, Peter |
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| bvnumber | BV009686530 |
| callnumber-first | Q - Science |
| callnumber-label | QA269 |
| callnumber-raw | QA269.M66 1994 |
| callnumber-search | QA269.M66 1994 |
| callnumber-sort | QA 3269 M66 41994 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | CC 3200 QH 430 SK 860 |
| classification_tum | MAT 920f |
| ctrlnum | (OCoLC)299786494 (DE-599)BVBBV009686530 |
| dewey-full | 519.3 519.320 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.3 519.3 20 |
| dewey-search | 519.3 519.3 20 |
| dewey-sort | 3519.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie Wirtschaftswissenschaften |
| format | Book |
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| spelling | Morris, Peter Verfasser aut Introduction to game theory Peter Morris New York [u.a.] Springer 1994 XVI, 230 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Literaturverz. S. 223 - 225 Spieltheorie - Lehrbuch Game theory Spieltheorie (DE-588)4056243-8 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Spieltheorie (DE-588)4056243-8 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006406028&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| subject_GND | (DE-588)4056243-8 (DE-588)4151278-9 |
| title | Introduction to game theory |
| title_auth | Introduction to game theory |
| title_exact_search | Introduction to game theory |
| title_full | Introduction to game theory Peter Morris |
| title_fullStr | Introduction to game theory Peter Morris |
| title_full_unstemmed | Introduction to game theory Peter Morris |
| title_short | Introduction to game theory |
| title_sort | introduction to game theory |
| topic | Spieltheorie - Lehrbuch Game theory Spieltheorie (DE-588)4056243-8 gnd |
| topic_facet | Spieltheorie - Lehrbuch Game theory Spieltheorie Einführung |
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