Dynamic noncooperative game theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London u.a.
Acad. Press
1995
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 519 S. graph. Darst. |
| ISBN: | 012080221X |
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MARC
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| 245 | 1 | 0 | |a Dynamic noncooperative game theory |c Tamer Başar ; Geert Jan Olsder |
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| 264 | 1 | |a London u.a. |b Acad. Press |c 1995 | |
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Record in the Search Index
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| adam_text | CONTENTS
Preface v
Chapter 1 Introduction and Motivation 1
1.1 Preliminary Remarks 1
1.2 Preview on Noncooperative Games 3
1.3 Outline of the Book 12
1.4 Conventions, Notation and Terminology 13
PART I
Chapter 2 Noncooperative Finite Games: Two Person Zero Sum 19
2.1 Introduction 19
2.2 Matrix Games 20
2.3 Computation of Mixed Equilibrium Strategies 31
2.4 Extensive Forms: Single Act Games 38
2.5 Extensive Games: Multi Act Games 48
2.6 Zero Sum Games with Chance Moves 60
2.7 Two Extensions 64
2.7.1 Games with repeated decisions 64
2.7.2 Extensive forms with cycles 66
2.8 Action Dependent Information Sets 69
2.8.1 Duels 69
2.8.2 A searchlight game 70
2.9 Problems 73
2.10 Notes 77
Chapter 3 Noncooperative Finite Games: TV Person Nonzero Sum 79
3.1 Introduction 79
3.2 Bimatrix Games 80
3.3 JV Person Games In Normal Form 90
3.4 Computation Of Mixed Strategy Nash Equilibria In Uimatrix Games 98
3.5 Nash Equilibria of jV Person Games in Extensive Form 100
3.5.1 Single act games: Pure strategy Nash equilibria 103
3.5.2 Single act games: Nash equilibria in behavioural and mixed
strategies 120
3.5.3 Multi act games: Pure strategy Nash equilibria 122
ix
x DYNAMIC NONCOOPERATIVE GAME THEORY
3.5.4 Multi act games: Behavioural and mixed equilibrium
strategies 129
3.5.5 Other refinements on Nash equilibria 131
3.6 The Stackelberg Equilibrium Solution 135
3.7 Nonzero Sum Games With Chance Moves 153
3.8 Problems 157
3.9 Notes 163
Chapter 4 Static Noncooperative Infinite Games 167
4.1 Introduction 167
4.2 e Equilibrium Solutions 167
4.3 Continuous Kernel Games: Reaction Curves, and Existence
and Uniqueness Of Nash and Saddle Point Equilibria 174
4.4 Stackelberg Solution Of Continuous Kernel Games 185
4.5 Consistent Conjectural Variations Equilibrium 192
4.6 Quadratic Games With Applications In Microeconomics 196
4.7 Problems 210
4.8 Notes 216
PART II
Chapter 5 General Formulation Of Infinite Dynamic Games 221
5.1 Introduction 221
5.2 Discrete Time Infinite Dynamic Games 222
5.3 Continuous Time Infinite Dynamic Games 230
5.4 Mixed and Behavioural Strategies In Infinite Dynamic Games 237
5.5 Tools For One Person Optimisation 239
5.5.1 Dynamic programming for discrete time systems 239
5.5.2 Dynamic programming for continuous time systems 242
5.5.3 The minimum principle 248
5.6 Representations Of Strategies Along Trajectories, and Time
Consistency Of Optimal Policies 253
5.7 Viscosity Solutions 261
5.8 Problems 267
5.9 Notes 269
Chapter 6 Nash and Saddle Point Equilibria Of Infinite Dynamic
Games 271
6.1 Introduction 271
6.2 Open Loop and Feedback Nash and Saddle Point Equilibria For
Dynamic Games In Discrete Time 272
6.2.1 Open Loop Nash equilibria 273
6.2.2 Closed loop no memory and feedback Nash equilibria 282
6.2.3 Linear quadratic games with an infinite number of stages 295
6.3 Informational Properties Of Nash Equilibria In Discrete Time
Dynamic Games 299
6.3.1 A three person dynamic game illustrating informational
xi
nonuniqueness 299
6.3.2 General results on informationally nonunique equilibrium
solutions 303
6.4 Stochastic Nonzero Sum Games With Deterministic Information
Patterns 310
6.5 Open Loop and Feedback Nash and Saddle Point Equilibria of
Differential Games 317
6.5.1 Open loop Nash equilibria 318
6.5.2 Closed loop no memory and feedback Nash equilibria 325
6.5.3 Linear quadratic differential games on an infinite time
horizon 340
6.6 Applications In Robust Controller Designs: ^T°° Optimal Control 345
6.7 Stochastic Differential Games With Deterministic Information
Patterns 353
6.8 Problems 358
6.9 Notes 365
Chapter 7 Stackelberg Equilibria Of Infinite Dynamic Games 367
7.1 Introduction 367
7.2 Open Loop Stackelberg Solution Of Two Person Dynamic Games
in Discrete Time 368
7.3 Feedback Stackelberg Solution Under Clps Information Pattern 375
7.4 (Global) Stackelberg Solution Under Clps Information Pattern 378
7.4.1 An illustrative example (Example 7.1) 378
7.4.2 A second example (Example 7.2): Follower acts twice
in the game 384
7.4.3 Linear Stackelberg solution of linear quadratic dynamic
games 387
7.4.4 Incentives (deterministic) 394
7.5 Stochastic Dynamic Games With Deterministic Information
Patterns 398
7.5.1 (Global) Stackelberg solutions 399
7.5.2 Feedback Stackelberg solutions 405
7.5.3 Stochastic incentive problems 406
7.6 Stackelberg Solution Of Differential Games 410
7.6.1 The open loop information structure 410
7.6.2 The CLPS information pattern 415
7.7 Problems 420
7.8 Notes 424
Chapter 8 Pursuit Evasion Games 427
8.1 Introduction 427
8.2 Necessary and Sufficient Conditions For Saddle Point Equilibria 428
8.2.1 The Isaacs equation 429
8.2.2 Upper and lower values, and viscosity solutions 436
8.3 Capturability 438
8.4 Singular Surfaces 446
8.5 Solution Of A pursuit Evasion Game: The Lady In The Lake 452
xii DYNAMIC NONCOOPERATIVE GAME THEORY
8.6 An Application In Maritime Collision Avoidance 456
8.7 Role Determination and An Application In Aeronautics 461
8.8 Problems 469
8.9 Notes 472
Appendix A Mathematical Review 475
A.I Sets 475
A.2 Normed Linear (Vector) Spaces 476
A.3 Matrices 477
A.4 Convex Sets and Functionals 477
A.5 Optimisation of Functionals 478
Appendix B Some Notions Of Probability Theory 481
B.I Ingredients of Probability Theory 481
B.2 Random Vectors 482
B.3 Integrals and Expectation 484
B.4 Norms, and the Cauchy Schwarz Inequality 485
Appendix C Fixed Point Theorems 487
References 489
List of Corollaries, Definitions, Examples, Lemmas, Propositions,
Remarks and Theorems 509
Index 515
|
| any_adam_object | 1 |
| author | Başar, Tamer 1946- Olsder, Geert Jan |
| author_GND | (DE-588)170065804 (DE-588)171061055 |
| author_facet | Başar, Tamer 1946- Olsder, Geert Jan |
| author_role | aut aut |
| author_sort | Başar, Tamer 1946- |
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| callnumber-subject | QA - Mathematics |
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| dewey-full | 519.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.3 |
| dewey-search | 519.3 |
| dewey-sort | 3519.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| indexdate | 2024-07-09T17:47:07Z |
| institution | BVB |
| isbn | 012080221X |
| language | English |
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| physical | XII, 519 S. graph. Darst. |
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| spelling | Başar, Tamer 1946- Verfasser (DE-588)170065804 aut Dynamic noncooperative game theory Tamer Başar ; Geert Jan Olsder 2. ed. London u.a. Acad. Press 1995 XII, 519 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Jeux non coopératifs (mathématiques) ram Mathématiques économiques ram Speltheorie gtt jeu dynamique inriac théorie jeu inriac Differential games Noncooperative games (Mathematics) Nichtkooperatives Spiel (DE-588)4042085-1 gnd rswk-swf Dynamisches Spiel (DE-588)4121154-6 gnd rswk-swf Differentialspiel (DE-588)4012253-0 gnd rswk-swf Spieltheorie (DE-588)4056243-8 gnd rswk-swf Spieltheorie (DE-588)4056243-8 s DE-604 Differentialspiel (DE-588)4012253-0 s 1\p DE-604 Nichtkooperatives Spiel (DE-588)4042085-1 s 2\p DE-604 Dynamisches Spiel (DE-588)4121154-6 s 3\p DE-604 Olsder, Geert Jan Verfasser (DE-588)171061055 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006731428&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Başar, Tamer 1946- Olsder, Geert Jan Dynamic noncooperative game theory Jeux non coopératifs (mathématiques) ram Mathématiques économiques ram Speltheorie gtt jeu dynamique inriac théorie jeu inriac Differential games Noncooperative games (Mathematics) Nichtkooperatives Spiel (DE-588)4042085-1 gnd Dynamisches Spiel (DE-588)4121154-6 gnd Differentialspiel (DE-588)4012253-0 gnd Spieltheorie (DE-588)4056243-8 gnd |
| subject_GND | (DE-588)4042085-1 (DE-588)4121154-6 (DE-588)4012253-0 (DE-588)4056243-8 |
| title | Dynamic noncooperative game theory |
| title_auth | Dynamic noncooperative game theory |
| title_exact_search | Dynamic noncooperative game theory |
| title_full | Dynamic noncooperative game theory Tamer Başar ; Geert Jan Olsder |
| title_fullStr | Dynamic noncooperative game theory Tamer Başar ; Geert Jan Olsder |
| title_full_unstemmed | Dynamic noncooperative game theory Tamer Başar ; Geert Jan Olsder |
| title_short | Dynamic noncooperative game theory |
| title_sort | dynamic noncooperative game theory |
| topic | Jeux non coopératifs (mathématiques) ram Mathématiques économiques ram Speltheorie gtt jeu dynamique inriac théorie jeu inriac Differential games Noncooperative games (Mathematics) Nichtkooperatives Spiel (DE-588)4042085-1 gnd Dynamisches Spiel (DE-588)4121154-6 gnd Differentialspiel (DE-588)4012253-0 gnd Spieltheorie (DE-588)4056243-8 gnd |
| topic_facet | Jeux non coopératifs (mathématiques) Mathématiques économiques Speltheorie jeu dynamique théorie jeu Differential games Noncooperative games (Mathematics) Nichtkooperatives Spiel Dynamisches Spiel Differentialspiel Spieltheorie |
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