Game theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey
World Scientific
[2016]
|
| Edition: | Second edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Literaturverzeichnis Seite 543-548 |
| Physical Description: | xii, 551 Seiten Diagramme |
| ISBN: | 9789814725385 |
Staff View
MARC
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Record in the Search Index
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Contents
A
Preface v
Acknowledgments vii
1 Matrix Games 1
1.1 Definition of a Two-Person Zero-Sum Game in
Normal Form . 1
1.2 Maximin and Minimax Strategies. 7
1.3 Saddle Points. . 10
1.4 Mixed Extension of a Game. 17
1.5 Convex Sets and Systems of Linear Inequalities . . 22
1.6 Existence of a Solution of the Matrix Game in
Mixed Strategies. 27
1.7 Properties of Optimal Strategies and Value of the
Game. 32
1.8 Dominance of Strategies. 44
1.9 Completely Mixed and Symmetric Games . 52
1.10 Iterative Methods of Solving Matrix Games . 59
1.11 Exercises and Problems. 65
IX
X
Game Theory
2 Infinite Zero-Sum Two-Person Games 71
2.1 Infinite Games. 71
2.2 e-Saddle Points, e-Optimal Strategies. 75
2.3 Mixed Strategies. 82
2.4 Games with Continuous Payoff Functions. 92
2.5 Games with a Convex Payoff Function . 101
2.6 Simultaneous Games of Pursuit. 115
2.7 One Class of Games with a Discontinuous Payoff
Function. 123
2.8 Infinite Simultaneous Search Games. 127
2.9 A Poker Model . 134
2.10 Exercises and Problems. 160
3 Nonzero-Sum Games 165
3.1 Definition of Noncooperative Game
in Normal Form. 165
3.2 Optimality Principles in Noncooperative
Games. 171
3.3 Mixed Extension of Noncooperative Game. 185
3.4 Existence of Nash Equilibrium. 191
3.5 Kakutani Fixed-Point Theorem and Proof
of Existence of an Equilibrium in n-Person
Games. 197
3.6 Refinements of Nash Equilibria. 202
3.7 Properties of Optimal Solutions. 207
3.8 Symmetric Bimatrix Games and Evolutionary
Stable Strategies. 213
3.9 Equilibrium in Joint Mixed Strategies. 218
3.10 The Bargaining Problem. 223
3.11 Exercises and Problems. 234
4 Cooperative Games 241
4.1 Games in Characteristic Function Form. 241
4.2 The Core and NM-Solution. 253
Contents xi
4.3 The Shapley Value. 265
4.4 The Potential of the Shapley Value. 274
4.5 The r-Value and Nucleolus. 279
4.6 Exercises and Problems. 282
5 Positional Games 287
5.1 Multistage Games with Perfect Information . 287
5.2 Absolute Equilibrium (Subgame-Perfect). 295
5.3 Fundamental Functional Equations. 306
5.4 Penalty Strategies. 309
5.5 Repeated Games and Equilibrium in Punishment
(Penalty) Strategies. 313
5.6 Hierarchical Games. 315
5.7 Hierarchical Games (Cooperative Version). 319
5.8 Multistage Games with Incomplete
Information. 328
5.9 Behavior Strategy. 337
5.10 Functional Equations for Simultaneous Multistage
Games. 347
5.11 Cooperative Multistage Games with Perfect
Information. 358
5.12 One-Way Flow Two-Stage Network Games. 377
5.13 Exercises and Problems. 391
6 N-Person Differential Games 401
6.1 Optimal Control Problem . 401
6.2 Differential Games and Their Solution
Concepts. 412
6.3 Application of Differential Games
in Economics. 421
6.4 Infinite-Horizon Differential Games. 424
6.5 Cooperative Differential Games in Characteristic
Function Form. 431
6.6 Imputation in a Dynamic Context. 436
xn
Game Theory
6.7 Principle of Dynamic Stability. 439
6.8 Dynamic Stable Solutions . 440
6.9 Payoff Distribution Procedure. 441
6.10 An Analysis in Pollution Control. 445
6.11 Illustration with Specific Functional Forms. 454
6.12 Exercises and Problems. 459
7 Zero-Sum Differential Games 463
7.1 Differential Zero-Sum Games with Prescribed
Duration. 463
7.2 Multistage Perfect-Information Games with an
Infinite Number of Alternatives. 476
7.3 Existence of e-Equilibria in Differential Games with
Prescribed Duration. 482
7.4 Differential Time-Optimal Games of Pursuit . 490
7.5 Necessary and Sufficient Condition for Existence of
Optimal Open-Loop Strategy for Evader. 499
7.6 Fundamental Equation. 504
7.7 Methods of Successive Approximations for Solving
Differential Games of Pursuit . 514
7.8 Examples of Solutions to Differential Games of
Pursuit. 519
7.9 Games of Pursuit with Delayed Information for
Pursuer. 525
7.10 Exercises and Problems. 534
Bibliography 543
Index 549
Reviews of the First Edition:
" This is a well-crafted textbook that covers a wide range of topics
in the theory of decisions in situations ctinflicl, known also as
game theory. recommend it to anyone who wishes to master, or to
teach, the mathematics of games. "
Mathematical Reviews
"A distinctive feature of the hook is its coverage of cooperative
differential games. In this respect, the book is a welcome alternative
or supplement to other existing books. "
Mathematics Abstracts
Game theory is a branch of modem applied mathematics that aims to
analyse various problems of conflict between parties that have opposed
similar or simply different interests.
Games arc grouped into several classes according to some important
features. In Came Theory (Second edition), Petrosyan and Zehkevich
consider zero-sum two-person games, strategic n-person games in
normal form, cooperative games, games in extensive form with complete
and incomplete information, differential pursuit games and differential
cooperative, and non-cooperative n-person games. The second edition
updates heavily from the 1st edition published in 1996.
ISBN 978 981 4725-38-5 |
| any_adam_object | 1 |
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| illustrated | Not Illustrated |
| indexdate | 2025-01-02T21:14:37Z |
| institution | BVB |
| isbn | 9789814725385 |
| language | English |
| lccn | 2015042776 |
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| physical | xii, 551 Seiten Diagramme |
| publishDate | 2016 |
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| spelling | Petrosjan, Leon A. 1940- Verfasser (DE-588)123918049 aut Game theory Leon A. Petrosyan, Nikolay A. Zenkevich, St. Petersburg State University, Russia Second edition New Jersey World Scientific [2016] © 2016 xii, 551 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Literaturverzeichnis Seite 543-548 aGame theory aProbabilities Spieltheorie (DE-588)4056243-8 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Spieltheorie (DE-588)4056243-8 s DE-604 Zenkević, Nikolaj A. Verfasser aut Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028967733&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028967733&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Petrosjan, Leon A. 1940- Zenkević, Nikolaj A. Game theory aGame theory aProbabilities Spieltheorie (DE-588)4056243-8 gnd |
| subject_GND | (DE-588)4056243-8 (DE-588)4123623-3 |
| title | Game theory |
| title_auth | Game theory |
| title_exact_search | Game theory |
| title_full | Game theory Leon A. Petrosyan, Nikolay A. Zenkevich, St. Petersburg State University, Russia |
| title_fullStr | Game theory Leon A. Petrosyan, Nikolay A. Zenkevich, St. Petersburg State University, Russia |
| title_full_unstemmed | Game theory Leon A. Petrosyan, Nikolay A. Zenkevich, St. Petersburg State University, Russia |
| title_short | Game theory |
| title_sort | game theory |
| topic | aGame theory aProbabilities Spieltheorie (DE-588)4056243-8 gnd |
| topic_facet | aGame theory aProbabilities Spieltheorie Lehrbuch |
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